{ A000012 {HHHT beats THHH,1/8, (1-n)^(-1), {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}}, A000071 {HHHT beats TTTH,1/2, n/(1-2n+n^3), {1,2,4,7,12,20,33,54,88,143,232,376,609,986,1596,2583,4180,6764,10945,17710,28656,46367,75024,121392,196417,317810,514228,832039,1346268,2178308,3524577,5702886,9227464,14930351,24157816,39088168,63245985,102334154,165580140,267914295,433494436,701408732,1134903169,1836311902,2971215072,4807526975,7778742048,12586269024,20365011073,32951280098}}, A000073 {HTTT beats TTTH,7/8, (1-n(1+n+n^2))^(-1), {1,2,4,7,13,24,44,81,149,274,504,927,1705,3136,5768,10609,19513,35890,66012,121415,223317,410744,755476,1389537,2555757,4700770,8646064,15902591,29249425,53798080,98950096,181997601,334745777,615693474,1132436852,2082876103,3831006429,7046319384,12960201916,23837527729,43844049029,80641778674,148323355432,272809183135,501774317241,922906855808,1697490356184,3122171529233,5742568741225,10562230626642}}, A000073 {HHHH beats HHHT,1/2, -(n/(-1+n+n^2+n^3)), {1,1,2,4,7,13,24,44,81,149,274,504,927,1705,3136,5768,10609,19513,35890,66012,121415,223317,410744,755476,1389537,2555757,4700770,8646064,15902591,29249425,53798080,98950096,181997601,334745777,615693474,1132436852,2082876103,3831006429,7046319384,12960201916,23837527729,43844049029,80641778674,148323355432,272809183135,501774317241,922906855808,1697490356184,3122171529233,5742568741225}}, A003476 {HTHT beats THHH,7/16, (1+n+2n^2)/(2-2n-4n^3), {1,2,3,5,9,15,25,43,73,123,209,355,601,1019,1729,2931,4969,8427,14289,24227,41081,69659,118113,200275,339593,575819,976369,1655555,2807193,4759931,8071041,13685427,23205289,39347371,66718225,113128803,191823545,325259995,551517601,935164691,1585684681,2688719883,4559049265,7730418627,13107858393,22225956923,37686794177,63902510963,108354424809,183728013163}}, A003479 {HTHT beats HTTT,1/2, n/((-1+n)(-1+n+2n^3)), {1,2,3,6,11,18,31,54,91,154,263,446,755,1282,2175,3686,6251,10602,17975,30478,51683,87634,148591,251958,427227,724410,1228327,2082782,3531603,5988258,10153823,17217030,29193547,49501194,83935255,142322350,241324739,409195250,693839951,1176489430,1994879931,3382559834,5735538695,9725298558,16490418227,27961495618,47412092735,80392929190,136315920427,231140105898}}, A005251 {HHTH beats TTTT,5/8, (1+(-1+n)n)/(1+n(-2+n-n^2)), {1,2,4,7,12,21,37,65,114,200,351,616,1081,1897,3329,5842,10252,17991,31572,55405,97229,170625,299426,525456,922111,1618192,2839729,4983377,8745217,15346786,26931732,47261895,82938844,145547525,255418101,448227521,786584466,1380359512,2422362079,4250949112,7459895657,13091204281,22973462017,40315615410,70748973084,124155792775,217878227876,382349636061,670976837021,1177482265857}}, A005314 {HHHT beats HTHH,1/2, n/(1+n(-2+n-n^2)), {1,2,3,5,9,16,28,49,86,151,265,465,816,1432,2513,4410,7739,13581,23833,41824,73396,128801,226030,396655,696081,1221537,2143648,3761840,6601569,11584946,20330163,35676949,62608681,109870576,192809420,338356945,593775046,1042002567,1828587033,3208946545,5631308624,9882257736,17342153393,30433357674,53406819691,93722435101,164471408185,288627200960,506505428836,888855064897}}, A078044 {HTHT beats HHHT,3/8, -((n(1+n))/(-1+n+2n^3)), {1,2,2,4,8,12,20,36,60,100,172,292,492,836,1420,2404,4076,6916,11724,19876,33708,57156,96908,164324,278636,472452,801100,1358372,2303276,3905476,6622220,11228772,19039724,32284164,54741708,92821156,157389484,266872900,452515212,767294180,1301039980,2206070404,3740658764,6342738724,10754879532,18236197060,30921674508,52431433572,88903827692,150747176708}}, A005251 {HHHH beats THHT,1/4, {-a(n)+a(n-1)+a(n-2)+a(n-4)=0, a(1)=1,a(2)=1,a(3)= 2,a(4)=4}, {1,1,2,4,7,12,21,37,65,114,200,351,616,1081,1897,3329,5842,10252,17991,31572,55405,97229,170625,299426,525456,922111,1618192,2839729,4983377,8745217,15346786,26931732}}, A014743 {HHTH beats HHHH,3/5, {-a(n)-a(1+n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=5,a(5)=9}, {1,2,3,5,9,17,31,56,101,183,332,602,1091,1977,3583,6494,11770,21332,38662,70071,126997,230170,417161,756064,1370293,2483524,4501148,8157897,14785402,26797116,48567190,88023351,159533840,289139709,524037855,949768105,1721363151,3119804805,5654345520,10247956285,18573433061,33662557302,61010140688,110574999795,200406529829,363217519987,658296747806,1193099408276,2162377685706,3919101143798}}, A077930 {HHTH beats HHHT,1/3, {-a(n)-a(2+n)-a(3+n)+a(4+n)=0, a(1)=1,a(2)=1,a(3)=2,a(4)=3}, {1,1,2,3,6,10,18,31,55,96,169,296,520,912,1601,2809,4930,8651,15182,26642,46754,82047,143983,252672,443409,778128,1365520,2396320,4205249,7379697,12950466,22726483,39882198,69988378,122821042,215535903,378239143,663763424,1164823609,2044122936,3587185688,6295072048,11047081345,19386276329,34020543362,59701891739,104769516446,183857684514,322647744322,566207320575}}, A079959 {HHHH beats HTTH,4/11, {-a(n)-a(2+n)-a(4+n)-a(5+n)+a(6+n)=0, a(1)=1,a(2)=1,a(3)=2,a(4)=3,a(5)=6,a(6)=10}, {1,1,2,3,6,10,19,33,60,106,191,340,610,1089,1950,3485,6236,11150,19946,35670,63802,114107,204091,365018,652857,1167652,2088402,3735179,6680529,11948378,21370166,38221375,68360472,122265404,218676571,391111728,699518937,1251117444,2237673424,4002168000,7158036932,12802434104,22897663397,40953382945,73246756698,131004741747,234307198774,419067757570,749519376439,1340545258701}}, A079976 {HHHH beats HHTH,2/5, {-a(n)-a(1+n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=1,a(3)=2,a(4)=3,a(5)=6}, {1,1,2,3,6,11,20,36,65,118,214,388,703,1274,2309,4185,7585,13747,24915,45156,81841,148329,268832,487232,883061,1600463,2900685,5257212,9528190,17268926,31298264,56725087,102808753,186330956,337706899,612061206,1109301945,2010502860,3643842660,6604113625,11969319436,21693237866,39316902822,71258096973,129148432856,234069087131,424227660675,768871747601,1393505938105,2525595205693}}, A116732 {HHTT beats HHHT,1/3, { a(n)-a(1+n)-a(2+n)-a(3+n)+a(4+n)=0, a(1)=1,a(2)=1,a(3)=2,a(4)=4}, {1,1,2,4,6,11,19,32,56,96,165,285,490,844,1454,2503,4311,7424,12784,22016,37913,65289,112434,193620,333430,574195,988811,1702816,2932392,5049824,8696221,14975621,25789274,44411292,76479966,131704911,226806895,390580480,672612320,1158294784,1994680689,3435007313,5915370466,10186763684,17542460774,30209587611,52023441603,89588726304,154279294744,265681875040}}, A123908 {HHHH beats TTTH,7/22, {-a(n)-2a(1+n)-2a(2+n)-a(3+n)+a(5+n)=0, a(1)=1,a(2)=1,a(3)=2,a(4)=3,a(5)=6}, {1,1,2,3,6,10,17,30,52,90,156,271,470,815,1414,2453,4255,7381,12804,22211,38529,66836,115940,201120,348881,605201,1049837,1821143,3159121,5480100,9506282,16490465,28605867,49622350,86079461,149321296,259026360,449330785,779450224,1352105558,2345485810,4068693936,7057928159,12243326896,21238393209,36842056896,63909597255,110863425265,192313824361,333605126776}}, A128588 {HHTH beats TTTH,7/16, {-a(n)-a(1+n)+a(2+n)=0, a(1)=1,a(2)=2,a(3)=4}, {1,2,4,6,10,16,26,42,68,110,178,288,466,754,1220,1974,3194,5168,8362,13530,21892,35422,57314,92736,150050,242786,392836,635622,1028458,1664080,2692538,4356618,7049156,11405774,18454930,29860704,48315634,78176338,126491972,204668310,331160282,535828592,866988874,1402817466,2269806340,3672623806,5942430146,9615053952,15557484098,25172538050}}, {HHTT beats TTTH,7/12, -((n(1+n+n^2))/(-1+n+n^2+n^3-n^4)), {1,2,4,7,12,21,36,62,107,184,317,546,940,1619,2788,4801,8268,14238,24519,42224,72713,125218,215636,371343,639484,1101245,1896436,3265822,5624019,9685032,16678437,28721666,49461116,85176187,146680532,252596169,434991772,749092286,1289999695,2221487584,3825587793,6587982786,11345058468,19537141463,33644594924,57938812069,99775489988,171821755518,295891462651,509549896088}}, {HTHH beats THHH,7/12, -((n(1+n+n^2))/(-1+n+n^2+n^4)), {1,2,4,6,11,19,34,59,104,182,320,561,985,1728,3033,5322,9340,16390,28763,50475,88578,155443,272784,478702,840064,1474209,2587057,4539968,7967089,13981266,24535412,43056646,75559147,132597059,232691618,408345323,716596088,1257538470,2206826176,3872709969,6796132233,11926380672,20929339081,36728429722,64453901036,113108711430,198491951547,348329092699,611274945282,1072712749411}}, {HHHT beats THTH,9/16, (1+n^2)/(2(-1+n)(-1+n+2n^3)), {1,2,4,7,12,21,36,61,104,177,300,509,864,1465,2484,4213,7144,12113,20540,34829,59056,100137,169796,287909,488184,827777,1403596,2379965,4035520,6842713,11602644,19673685,33359112,56564401,95911772,162629997,275758800,467582345,792842340,1344359941,2279524632,3865209313,6553929196,11112978461,18843397088,31951255481,54177212404,91864006581,155766517544,264120942353}}, {HTTT beats HHHT,3/7, (n(1+n))/((-1+n)(-1+n+n^2)(1+n+n^2)), {1,2,3,6,10,16,27,44,71,116,188,304,493,798,1291,2090,3382,5472,8855,14328,23183,37512,60696,98208,158905,257114,416019,673134,1089154,1762288,2851443,4613732,7465175,12078908,19544084,31622992,51167077,82790070,133957147,216747218,350704366,567451584,918155951,1485607536,2403763487,3889371024,6293134512,10182505536,16475640049,26658145586}}, {HHHT beats HTHT,5/8, (n+n^3)/((-1+n)(-1+n+2n^3)), {1,2,4,8,14,24,42,72,122,208,354,600,1018,1728,2930,4968,8426,14288,24226,41080,69658,118112,200274,339592,575818,976368,1655554,2807192,4759930,8071040,13685426,23205288,39347370,66718224,113128802,191823544,325259994,551517600,935164690,1585684680,2688719882,4559049264,7730418626,13107858392,22225956922,37686794176,63902510962,108354424808,183728013162,311533035088}}, {HTTT beats TTHT,7/12, (n-n^3+n^4)/(1-2n+n^3-n^4+n^5), {1,2,3,6,11,20,35,62,109,192,337,592,1039,1824,3201,5618,9859,17302,30363,53284,93507,164094,287965,505344,886817,1556256,2731039,4792640,8410497,14759394,25900931,45452966,79764395,139976756,245642083,431071806,756478285,1327526848,2329647217,4088245872,7174371375,12590144096,22094162689,38772552658,68041086723,119403783478,209539032891,367715369028,645295488643,1132414641150}}, {HHHT beats HHTT,2/3, n/(1-2n+2n^4-n^5), {1,2,4,8,14,25,44,76,132,228,393,678,1168,2012,3466,5969,10280,17704,30488,52504,90417,155706,268140,461760,795190,1369385,2358196,4061012,6993404,12043228,20739449,35715070,61504344,105915636,182395602,314100513,540907408,931487888,1604100208,2762394992,4757075681,8192082994,14107453460,24294217144,41836677918,72046265529,124069707132,213658433436,367937728180,633619603220}}, {HHHT beats HHTH,2/3, n/(1-2n+n^3-n^4+n^5), {1,2,4,7,13,23,41,72,127,223,392,688,1208,2120,3721,6530,11460,20111,35293,61935,108689,190736,334719,587391,1030800,1808928,3174448,5570768,9776017,17155714,30106180,52832663,92714861,162703239,285524281,501060184,879299327,1543062751,2707886360,4752009296,8339194984,14634267032,25681348377,45067624706,79088168068,138790059807,243559576253,427417260767,750065005089,1316272325664}}, {HHTH beats THHH,5/12, -((n(-1+n^2+n^3))/(1-2n+n^3-n^4+n^5)), {1,2,3,4,7,12,21,36,63,110,193,338,593,1040,1825,3202,5619,9860,17303,30364,53285,93508,164095,287966,505345,886818,1556257,2731040,4792641,8410498,14759395,25900932,45452967,79764396,139976757,245642084,431071807,756478286,1327526849,2329647218,4088245873,7174371376,12590144097,22094162690,38772552659,68041086724,119403783479,209539032892,367715369029,645295488644}}, {HHHH beats TTHH,1/4, { a(n)-a(2+n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=1,a(3)=1,a(4)=2,a(5)=4}, {1,1,1,2,4,6,11,20,35,62,111,197,350,623,1108,1970,3504,6232,11083,19711,35056,62346,110881,197200,350716,623741,1109311,1972887,3508739,6240221,11098106,19737755,35103195,62430317,111031046,197466452,351190060,624584363,1110810558,1975553935,3513482404,6248656837,11113108813,19764437496,35150649211,62514713116,111181142986,197733396500,351664815106,625428705381}}, {HHTT beats HHHH,3/5, { a(n)-a(2+n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=6,a(5)=11}, {1,2,3,6,11,19,34,61,108,192,342,608,1081,1923,3420,6082,10817,19238,34214,60849,108219,192465,342295,608765,1082676,1925517,3424493,6090391,10831636,19263844,34260354,60931341,108365148,192725207,342757852,609587853,1084139571,1928120128,3429122345,6098624192,10846278812,19289885778,34306668654,61013710899,108511641139,192985741880,343221208140,610411922505,1085605161626,1930726651132}}, {HHHH beats HHTT,2/5, { a(n)-a(2+n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=1,a(3)=2,a(4)=4,a(5)=7}, {1,1,2,4,7,12,22,39,69,123,219,389,692,1231,2189,3893,6924,12314,21900,38949,69270,123195,219100,389665,693011,1232506,2191987,3898404,6933232,12330612,21929742,39001599,69363549,123361658,219396194,390191659,693947912,1234172216,2194950129,3903674063,6942604749,12347281029,21959387625,39054323274,69457317865,123528424015,219692784125,390719138380,694886023246,1235840627886}}, {HHTT beats TTTT,3/4, { a(n)-a(2+n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=8,a(5)=14}, {1,2,4,8,14,25,45,80,142,253,450,800,1423,2531,4501,8005,14237,25320,45031,80087,142433,253314,450514,801230,1424971,2534282,4507169,8015908,14256129,25354235,45091990,80195185,142625502,253656548,451123000,802313060,1426897423,2537707981,4513261916,8026744320,14275401157,25388509970,45152947466,80303596677,142818309793,253999452779,451732849279,803397664385,1428826369766,2541138573637}}, {HTHT beats HHTT,4/9, {(-5-n)a(n)+(-3-n)a(2+n)+(2+n)a(3+n)=0, a(1)=1,a(2)=2,a(3)=3}, {1,2,3,6,11,18,30,50,81,130,208,330,520,816,1275,1984,3077,4758,7337,11286,17322,26532,40563,61908,94336,143540,218112,331008,501749,759726,1149159,1736534,2621751,3954826,5960902,8977686,13511461,20320854,30542064,45875998,68867816,103324368,154937327,232213068,347859849,520856550,779536917,1166186478,1743892114,2606745416}}, {HHHT beats TTHH,5/12, {1+a(n)-a(1+n)-a(2+n)-a(3+n)+a(4+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=5}, {1,2,3,5,8,13,22,37,63,108,185,318,547,941,1620,2789,4802,8269,14239,24520,42225,72714,125219,215637,371344,639485,1101246,1896437,3265823,5624020,9685033,16678438,28721667,49461117,85176188,146680533,252596170,434991773,749092287,1289999696,2221487585,3825587794,6587982787,11345058469,19537141464,33644594925,57938812070,99775489989,171821755519,295891462652}}, {HHHH beats HTTT,4/11, {-1-a(n)-2a(1+n)-2a(2+n)-a(3+n)+a(5+n)=0,a(1)=1,a(2)=1,a(3)=2,a(4)=4,a(5)=7}, {1,1,2,4,7,12,21,37,64,111,193,335,581,1008,1749,3034,5263,9130,15838,27474,47659,82674,143414,248779,431555,748615,1298616,2252698,3907736,6778716,11758980,20398201,35384583,61381330,106477662,184705879,320407690,555808447,964156103,1672513248,2901294257,5032850039,8730441407,15144621153,26271243248,45572498303,79054218408,137134668513,237886322664,412659345184}}, {HHTT beats THHT,5/12, {-1-a(n)-a(2+n)-a(3+n)+a(4+n)=0, a(1)=1,a(2)=1,a(3)=2,a(4)=4}, {1,1,2,4,8,14,25,44,78,137,241,423,743,1304,2289,4017,7050,12372,21712,38102,66865,117340,205918,361361,634145,1112847,1952911,3427120,6014177,10554145,18521234,32502500,57037912,100094558,175653705,308250764,540942382,949287705,1665883793,2923422263,5130248439,9002958408,15799090641,27725471313,48654810394,85383240116,149837141152,262945852582,461437804129,809766896828}}, {HHHT beats HTTH,4/7, {-1-a(n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=7,a(5)=12}, {1,2,4,7,12,21,36,62,106,181,309,527,899,1533,2614,4457,7599,12956,22089,37660,64207,109467,186631,318188,542480,924876,1576824,2688332,4583345,7814158,13322380,22713363,38724076,66020785,112559020,191902186,327174570,557800833,950996189,1621356043,2764254419,4712785033,8034840286,13698621509,23354817839,39817693768,67885296641,115737830696,197321748847,336414397383}}, {HTTT beats THHT,1/2, {-1-a(n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=6,a(5)=10}, {1,2,3,6,10,18,31,53,91,155,265,452,771,1315,2242,3823,6518,11113,18947,32303,55074,93896,160084,272928,465316,793319,1352532,2305936,3931397,6702650,11427367,19482550,33215854,56629802,96548307,164605477,280636335,478457667,815723805,1390729780,2371059063,4042425179,6891941910,11750090895,20032762586,34153912545,58229100311,99274954767,169254145974,288561863328}}, {HHTT beats HTHT,5/9, {-2a(n)+(-4-n)a(1+n)-2a(2+n)-na(3+n)+(1+n)a(4+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=8}, {1,2,4,8,14,24,41,68,111,180,289,460,728,1146,1795,2800,4352,6742,10414,16044,24659,37818,57885,88440,134899,205448,312448,474548,719861,1090734,1650908,2496260,3770910,5691360,8582653,12932512,19472363,29298540,44053525,66196852,99409880,149200366,223805143,335537436,502797176,753069618,1127396766,1687043028,2523429031,3772931894}}, {HHTH beats HTTH,1/2, {-2a(n)+2a(1+n)-2a(3+n)+a(4+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=6}, {1,2,4,6,10,16,28,48,84,144,248,424,728,1248,2144,3680,6320,10848,18624,31968,54880,94208,161728,277632,476608,818176,1404544,2411136,4139136,7105536,12197888,20939776,35946752,61708800,105933824,181853696,312183296,535916544,919993344,1579327488,2711188480,4654223360,7989778432,13715834880,23545600000,40420089856,69388066816,119116603392,204484227072,351032500224}}, {HTHH beats TTHT,7/16, {-2a(n)+2a(1+n)-2a(3+n)+a(4+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=5}, {1,2,3,5,8,14,24,42,72,124,212,364,624,1072,1840,3160,5424,9312,15984,27440,47104,80864,138816,238304,409088,702272,1205568,2069568,3552768,6098944,10469888,17973376,30854400,52966912,90926848,156091648,267958272,459996672,789663744,1355594240,2327111680,3994889216,6857917440,11772800000,20210044928,34694033408,59558301696,102242113536,175516250112,301303963648}}, {HHTH beats THTT,9/16, {-2a(n)+2a(1+n)-2a(3+n)+a(4+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=7}, {1,2,4,7,12,20,34,58,100,172,296,508,872,1496,2568,4408,7568,12992,22304,38288,65728,112832,193696,332512,570816,979904,1682176,2887744,4957312,8510080,14609024,25078912,43052288,73906688,126873600,217800448,373892096,641850368,1101847040,1891510784,3247105024,5574216704,9569105920,16427023360,28199823360,48409868288,83103901696,142662203392,244904316928,420420567040}}, {HHHT beats THHT,9/16, {-2-a(n)-a(1+n)+a(2+n)=0, a(1)=1,a(2)=2,a(3)=4}, {1,2,4,8,14,24,40,66,108,176,286,464,752,1218,1972,3192,5166,8360,13528,21890,35420,57312,92734,150048,242784,392834,635620,1028456,1664078,2692536,4356616,7049154,11405772,18454928,29860702,48315632,78176336,126491970,204668308,331160280,535828590,866988872,1402817464,2269806338,3672623804,5942430144,9615053950,15557484096,25172538048,40730022146}}, {HTTT beats HHHH,7/11, {-3-a(n)-2a(1+n)-2a(2+n)-a(3+n)+a(5+n)=0,a(1)=1,a(2)=2,a(3)=4,a(4)=7,a(5)=13}, {1,2,4,7,13,23,40,70,122,212,368,639,1109,1924,3338,5791,10046,17427,30231,52442,90971,157807,273747,474867,823748,1428949,2478786,4299929,7459050,12939150,22445432,38935897,67541764,117164114,203243575,352564871,611591231,1060922016,1840372240,3192477798,5537963608,9606657544,16664585703,28907912599,50146305808,86988362704,150897959959,261761385224,454075209585,787680336361}}, {HHHT beats TTTT,15/22,{-4-a(n)-2a(1+n)-2a(2+n)-a(3+n)+a(5+n)=0,a(1)=1,a(2)=2,a(3)=4,a(4)=8,a(5)=14}, {1,2,4,8,14,25,44,77,134,233,405,703,1220,2117,3673,6372,11054,19176,33265,57705,100101,173645,301221,522526,906422,1572363,2727565,4731484,8207665,14237766,24698130,42843633,74320480,128923094,223641776,387949454,672972561,1167399678,2025078119,3512885488,6093772055,10570813647,18337098951,31809206856,55179155847,95718804111,166042581112,288032628472,499647707888,866734554769}}, {HHHT beats HTTT,4/7, {-4-n-a(n)-2a(1+n)-a(2+n)+a(4+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=8}, {1,2,4,8,14,24,41,68,112,184,300,488,793,1286,2084,3376,5466,8848,14321,23176,37504,60688,98200,158896,257105,416010,673124,1089144,1762278,2851432,4613721,7465164,12078896,19544072,31622980,51167064,82790057,133957134,216747204,350704352,567451570,918155936,1485607521,2403763472,3889371008,6293134496,10182505520,16475640032,26658145569,43133785618}}, {HHTH beats THTH,9/16, {-a(n)+a(1+n)-2a(2+n)+a(3+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=6}, {1,2,4,6,10,18,32,56,98,172,302,530,930,1632,2864,5026,8820,15478,27162,47666,83648,146792,257602,452060,793310,1392162,2443074,4287296,7523680,13203138,23169892,40660326,71353898,125217362,219741152,385618840,676713890,1187550092,2084005134,3657174066,6417893090,11262617248,19764515472,34684306786,60866715348,106813639382,187444870202,328942816370,577254401920,1013010857672}}, {HTHT beats THHT,7/16, {-a(n)+a(1+n)-2a(2+n)+a(3+n)=0, a(1)=1,a(2)=2,a(3)=2,a(4)=4}, {1,2,2,4,8,14,24,42,74,130,228,400,702,1232,2162,3794,6658,11684,20504,35982,63144,110810,194458,341250,598852,1050912,1844222,3236384,5679458,9966754,17490434,30693572,53863464,94523790,165877688,291095050,510836202,896455042,1573168932,2760719024,4844724158,8501898224,14919791314,26182408562,45946924034,80631230820,141497946168,248311585550,435756455752,764699272122}}, {HHTH beats THHT,5/12, {-a(n)+a(2+n)-2a(4+n)+a(5+n)=0, a(1)=1,a(2)=1,a(3)=2,a(4)=4,a(5)=7}, {1,1,2,4,7,13,23,41,73,130,232,414,739,1319,2354,4201,7497,13379,23876,42609,76040,135701,242172,432180,771268,1376404,2456329,4383562,7822900,13960739,24914320,44462069,79346961,141602502,252703674,450974707,804808981,1436261249,2563150293,4574195279,8163104016,14567866720,25997799410,46395645097,82797618753,147760542112,263693305847,470586792351,839808687687,1498721688280}}, {HTHH beats THHT,7/12, {-a(n)+a(2+n)-2a(4+n)+a(5+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=6,a(5)=10}, {1,2,3,6,10,18,32,57,102,182,325,580,1035,1847,3296,5882,10497,18733,33431,59661,106471,190008,339088,605136,1079925,1927233,3439338,6137839,10953581,19547749,34884892,62255541,111101172,198271033,353834274,631452268,1126889044,2011044986,3588908737,6404762704,11429932690,20397845687,36401973656,64962923359,115932763735,206893486504,369221895336,658913000593,1175895438041,2098501744481}}, {HHTT beats HTHH,3/7, {-a(n)+a(3+n)-2a(5+n)+a(6+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=5,a(5)=8,a(6)=13}, {1,2,3,5,8,13,22,38,66,115,200,347,601,1040,1799,3112,5384,9316,16121,27898,48279,83549,144584,250205,432982,749278,1296630,2243827,3882960,6719495,11628145,20122608,34822351,60260384,104281120,180459384,312286529,540414546,935192059,1618357973,2800582520,4846432365,8386793286,14513418598,25115596890,43462758467,75212680856,130156197187,225236429193,389773596128}}, {HHTT beats TTHT,9/14, {-a(n)+a(3+n)-2a(5+n)+a(6+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=8,a(5)=14,a(6)=24}, {1,2,4,8,14,24,41,70,120,207,358,620,1074,1860,3220,5573,9644,16688,28877,49970,86472,149640,258954,448124,775485,1341986,2322320,4018795,6954558,12034920,20826530,36040488,62368376,107929017,186772104,323210752,559319017,967906418,1674970460,2898550920,5015967526,8680175344,15021118785,25994176462,44983148040,77843728215,134709247494,233115522292,403408435154,698101799276}}, {HHTH beats TTHH,5/14, {-a(n)+a(3+n)-2a(5+n)+a(6+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=4,a(5)=6,a(6)=9}, {1,2,3,4,6,9,15,26,46,81,142,247,428,740,1279,2211,3824,6616,11449,19814,34291,59344,102698,177721,307547,532210,920990,1593777,2758042,4772815,8259400,14292968,24734111,42802599,74070272,128179248,221815297,383853290,664261443,1149510188,1989237358,3442392521,5957090151,10308796234,17839461390,30871342817,53423126758,92449184647,159984116628,276853902732}}, {HTHH beats HHTT,4/7, {-a(n)+a(3+n)-2a(5+n)+a(6+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=7,a(5)=12,a(6)=20}, {1,2,4,7,12,20,34,58,100,173,300,520,901,1560,2700,4672,8084,13988,24205,41886,72484,125435,217068,375640,650050,1124918,1946680,3368745,5829640,10088240,17457785,30210848,52280136,90471232,156561256,270930616,468847785,811345162,1404039844,2429703135,4204622364,7276135500,12591415650,21789554098,37707012540,65252312565,112919693396,195408509752,338156122589,585182105880}}, {HHHH beats HTHT,5/12, {-a(n)-2a(1+n)-a(3+n)+a(4+n)=0, a(1)=1,a(2)=1,a(3)=2,a(4)=4}, {1,1,2,4,7,12,22,40,71,127,229,411,736,1321,2372,4255,7633,13698,24580,44101,79130,141988,254770,457131,820237,1471765,2640797,4738402,8502169,15255528,27373129,49115869,88129094,158130880,283735747,509109804,913500658,1639103032,2941058387,5277169507,9468876229,16990096035,30485493436,54700415401,98149483700,176110566607,315996890845,566996273646,1017366890560,1825471238857}}, {HTHT beats HHHH,7/12, {-a(n)-2a(1+n)-a(3+n)+a(4+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=5}, {1,2,3,5,10,18,31,56,102,182,325,585,1051,1883,3378,6065,10882,19521,35029,62858,112782,202361,363106,651528,1169032,2097605,3763767,6753359,12117601,21742740,39013225,70001786,125604867,225374057,404390854,725602374,1301955355,2336111120,4191706722,7521219806,13495397401,24214921965,43449068299,77961082907,139886324238,250999382801,450370616914,808104348297,1449989438137,2601730054766}}, {HTHT beats TTTT,5/8, {-a(n)-2a(1+n)-a(3+n)+a(4+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=6}, {1,2,3,6,11,19,34,62,111,198,356,640,1147,2057,3693,6627,11888,21331,38278,68681,123231,221118,396758,711901,1277368,2292002,4112562,7379199,13240571,23757697,42628657,76488998,137244963,246259974,441866627,792845551,1422610462,2552603690,4580161419,8218227894,14746045736,26458972264,47475589471,85185908837,152849899101,274260050307,492107457452,882993164491,1584363164206,2842838129417}}, {HHHH beats THTH,3/8, {-a(n)-2a(1+n)-a(3+n)+a(4+n)=0, a(1)=1,a(2)=1,a(3)=2,a(4)=3}, {1,1,2,3,6,11,19,34,62,111,198,356,640,1147,2057,3693,6627,11888,21331,38278,68681,123231,221118,396758,711901,1277368,2292002,4112562,7379199,13240571,23757697,42628657,76488998,137244963,246259974,441866627,792845551,1422610462,2552603690,4580161419,8218227894,14746045736,26458972264,47475589471,85185908837,152849899101,274260050307,492107457452,882993164491,1584363164206}}, {HTTT beats TTTT,15/16,{-a(n)-a(1+n)-a(2+n)+a(3+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=8}, {1,2,4,8,14,26,48,88,162,298,548,1008,1854,3410,6272,11536,21218,39026,71780,132024,242830,446634,821488,1510952,2779074,5111514,9401540,17292128,31805182,58498850,107596160,197900192,363995202,669491554,1231386948,2264873704,4165752206,7662012858,14092638768,25920403832,47675055458,87688098058,161283557348,296646710864,545618366270,1003548634482,1845813711616,3394980712368,6244343058466,11485137482450}}, {HHHH beats HTHH,3/10, {-a(n)-a(1+n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=1,a(3)=1,a(4)=2,a(5)=4}, {1,1,1,2,4,8,14,25,45,82,149,270,489,886,1606,2911,5276,9562,17330,31409,56926,103173,186991,338903,614229,1113231,2017624,3656749,6627505,12011714,21770074,39456161,71510489,129605869,234898146,425730250,771595046,1398441654,2534540715,4593610765,8325476776,15089124241,27347583386,49564859107,89831530034,162810990158,295079227819,534802660470,969278277430,1756723458092}}, {HTHH beats HHHH,7/10, {-a(n)-a(1+n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=6,a(5)=11}, {1,2,4,6,11,20,37,67,121,219,397,720,1305,2365,4286,7768,14079,25517,46247,83818,151912,275326,499002,904393,1639125,2970756,5384209,9758360,17686087,32054328,58095380,105292277,190832104,345864796,626846608,1136099061,2059070050,3731866011,6763647465,12258459145,22217275721,40266670927,72979460124,132268237661,239723432651,434475616960,787445180662,1427168495407,2586605346381,4687972891399}}, {HTTH beats HHHH,7/11, {-a(n)-a(2+n)-a(4+n)-a(5+n)+a(6+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=6,a(5)=11,a(6)=19}, {1,2,4,6,11,19,35,62,112,199,357,637,1141,2039,3649,6524,11671,20871,37332,66766,119418,213579,382000,683216,1221966,2185527,3908911,6991233,12504110,22364086,39999073,71539919,127952013,228847251,409302447,732053703,1309307236,2341748109,4188309805,7490958868,13397878356,23962639036,42858134433,76653480446,137097803040,245204881390,438558697219,784379698091,1402894332783,2509132392710}}, {HHTH beats HTHT,5/7, {-a(n)-a(3+n)+a(4+n)-2a(5+n)+a(6+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=7,a(5)=12,a(6)=21}, {1,2,4,7,12,21,38,69,125,226,408,736,1328,2397,4327,7811,14100,25452,45943,82931,149698,270219,487771,880473,1589337,2868903,5178640,9347933,16873900,30458980,54981330,99246483,179149256,323381292,583733711,1053694366,1902017643,3433321114,6197468207,11187014235,20193615088,36451378514,65798173818,118771905324,214394483551,387002249831,698575536523,1260994685280,2276214257686,4108781271939}}, {HTHT beats HHTH,2/7, {-a(n)-a(3+n)+a(4+n)-2a(5+n)+a(6+n)=0, a(1)=1,a(2)=1,a(3)=1,a(4)=2,a(5)=4,a(6)=7}, {1,1,1,2,4,7,13,24,43,77,139,251,453,818,1477,2666,4812,8686,15679,28302,51088,92219,166464,300483,542400,979083,1767337,3190210,5758630,10394870,18763720,33870283,61139053,110361753,199213366,359598902,649109911,1171704569,2115037182,3817841459,6891563671,12439921967,22455231633,40533809539,73167346594,132073956741,238405940098,430345192016,776813632308,1402221822237}}, {HTTH beats HHHT,3/7, {-a(n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=5,a(5)=8}, {1,2,3,5,8,14,24,41,70,119,203,346,590,1006,1715,2924,4985,8499,14490,24704,42118,71807,122424,208721,355849,606688,1034344,1763456,3006521,5125826,8739035,14899205,25401696,43307422,73834944,125881401,214615550,365898647,623821619,1063555210,1813258230,3091428990,5270585867,8985836476,15319977553,26119072259,44530478802,75920136928,129436452206,220676566687}}, {HTHH beats THTH,5/14, {-a(n)-a(3+n)+a(4+n)-2a(5+n)+a(6+n)=0, a(1)=1,a(2)=1,a(3)=2,a(4)=3,a(5)=5,a(6)=9}, {1,1,2,3,5,9,17,31,56,101,182,328,592,1069,1930,3484,6289,11352,20491,36988,66767,120521,217552,392702,708864,1279566,2309737,4169293,7525967,13585080,24522350,44265153,79902773,144232036,260352419,469960655,848323277,1531303471,2764147093,4989546028,9006600853,16257763426,29346795304,52973731506,95622578227,172607766280,311573286692,562419148757,1015219572406,1832567014253}}, {HTTH beats THHH,1/2, {-a(n)-a(3+n)-a(4+n)+a(5+n)=0, a(1)=1,a(2)=2,a(3)=4,a(4)=6,a(5)=10}, {1,2,4,6,10,17,29,50,85,145,247,421,718,1224,2087,3558,6066,10342,17632,30061,51251,87378,148971,253981,433013,738245,1258636,2145852,3658469,6237334,10634048,18130018,30909918,52698405,89845657,153178110,261153785,445241813,759094003,1294181473,2206453586,3761788844,6413484243,10934367090,18642032806,31782853482,54186675132,92383012857,157504055079,268529100742}}, {HTHT beats THTT,9/14, {-a(n)-a(3+n)+a(4+n)-2a(5+n)+a(6+n)=0, a(1)=1,a(2)=2,a(3)=3,a(4)=6,a(5)=11,a(6)=19}, {1,2,3,6,11,19,34,62,112,202,365,659,1189,2146,3874,6993,12623,22786,41131,74245,134019,241917,436683,788254,1422873,2568420,4636240,8368850,15106563,27268770,49222700,88851613,160385536,289511009,522594658,943332613,1702804277,3073722212,5548358296,10015309666,18078577906,32633537055,58906610147,106331983357,191939251918,346468440292,625408189929,1128920728539,2037808317588,3678436079923}}}