[seqfan] Re: Similar sequences A126222 and A166073

Richard Mathar mathar at strw.leidenuniv.nl
Sat Aug 21 23:45:05 CEST 2010


Observed in http://list.seqfan.eu/pipermail/seqfan/2010-August/005716.html

jg> I noticed sequences A126222 and A166073 appear identical with zeros removed:


These seem to be even closer: A166073 appears to be a variant of A126222
where zeros are sorted to the start of each row:

A126222:

1
0,1
1,0,1
0,4,0,1
2,0,11,0,1
0,15,0,26,0,1
5,0,69,0,57,0,1
0,56,0,252,0,120,0,1
14,0,364,0,804,0,247,0,1
0,210,0,1800,0,2349,0,502,0,1
42,0,1770,0,7515,0,6455,0,1013,0,1
0,792,0,11055,0,27940,0,16962,0,2036,0,1
132,0,8217,0,57035,0,95458,0,43086,0,4083,0,1
0,3003,0,62062,0,257257,0,305812,0,106587,0,8178,0,1
429,0,37037,0,381381,0,1049685,0,931385,0,258153,0,16369,0,1
0,11440,0,328328,0,2022384,0,3962140,0,2723280,0,614520,0,32752,0,1
1430,0,163592,0,2341976,0,9591764,0,14051660,0,7699800,0,1441928,0,65519,0,1
0,43758,0,1665456,0,14275716,0,41666184,0,47352820,0,21167312,0,3342489,0,131054,0,1
4862,0,712062,0,13527852,0,77161980,0,168567444,0,152915748,0,56818743,0,7667883,0,262125,0,1
0,167960,0,8188050,0,93194544,0,379080552,0,642966384,0,476287725,0,149420940,0,17432766,0,524268,0,1
16796,0,3065270,0,74622690,0,565469640,0,1722610680,0,2333765763,0,1438193505,0,386005710,0,39321810,0,1048555,0,1
0,646646,0,39296180,0,573347610,0,3099637200,0,7334830965,0,8119195938,0,4227406995,0,981727740,0,88080615,0,2097130,0,1
58786,0,13082146,0,397118810,0,3858877770,0,15629771355,0,29554854483,0,27229650063,0,12136293015,0,2462578965,0,196083965,0,4194281,0,1

A166073 (without the first entry probably tabl instead of tabf):

1
1,1
0,4,1
0,2,11,1
0,0,15,26,1
0,0,5,69,57,1
0,0,0,56,252,120,1
0,0,0,14,364,804,247,1
0,0,0,0,210,1800,2349,502,1
0,0,0,0,42,1770,7515,6455,1013,1
0,0,0,0,0,792,11055,27940,16962,2036,1
0,0,0,0,0,132,8217,57035,95458,43086,4083,1
0,0,0,0,0,0,3003,62062,257257,305812,106587,8178,1
0,0,0,0,0,0,429,37037,381381,1049685,931385,258153,16369,1
0,0,0,0,0,0,0,11440,328328,2022384,3962140,2723280,614520,32752,1
0,0,0,0,0,0,0,1430,163592,2341976,9591764,14051660,7699800,1441928,65519,1
0,0,0,0,0,0,0,0,43758,1665456,14275716,41666184,47352820,21167312,3342489,131054,1
0,0,0,0,0,0,0,0,4862,712062,13527852,77161980,168567444,152915748,56818743,7667883,262125,1
0,0,0,0,0,0,0,0,0,167960,8188050,93194544,379080552,642966384,476287725,149420940,17432766,524268,1
0,0,0,0,0,0,0,0,0,16796,3065270,74622690,565469640,1722610680,2333765763,1438193505,386005710,39321810,1048555,1
0,0,0,0,0,0,0,0,0,0,646646,39296180,573347610,3099637200,7334830965,8119195938,4227406995,981727740,88080615,2097130,1
0,0,0,0,0,0,0,0,0,0,58786,13082146,397118810,3858877770,15629771355,29554854483,27229650063,12136293015,2462578965,196083965,4194281,1

(Both triangles from Emeric's Maple implementations)




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