# [seqfan] Passing Through Powers of Ten

Ron Hardin rhhardin at att.net
Wed Nov 12 03:07:27 CET 2014

```For some reason these have a many-powers-of-ten stage, like a layer of atmosphere that must be passed through

/tmp/ema
T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column
Table starts
...16....36.....81.....144......256......400......625......900.....1296
...36...108....324.....720.....1600.....3000.....5625.....9450....15876
...81...324...1296....3600....10000....22500....50625....99225...194481
..144...720...3600...12000....40000...105000...275625...617400..1382976
..256..1600..10000...40000...160000...490000..1500625..3841600..9834496
..400..3000..22500..105000...490000..1715000..6002500.17287200.49787136
..625..5625..50625..275625..1500625..6002500.24010000.77792400.........
..900..9450..99225..617400..3841600.17287200.77792400..................
.1296.15876.194481.1382976..9834496.49787136...........................
.1764.24696.345744.2765952.22127616....................................

/tmp/emb
T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column
Table starts
.....81......324.......1296.........3600.........10000..........22500
....324.....2160......14400........60000........250000.........787500
...1296....14400.....160000......1000000.......6250000.......27562500
...3600....60000....1000000......8750000......76562500......450187500
..10000...250000....6250000.....76562500.....937890625.....7353062500
..22500...787500...27562500....450187500....7353062500....74118870000
..50625..2480625..121550625...2647102500...57648010000...747118209600
..99225..6482700..423536400..11859019200..332052537600..5379251109120
.194481.16941456.1475789056..53128406016.1912622616576.38730607985664
.345744.38723328.4337012736.195165573120.8782450790400...............

/tmp/emc
T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column
Table starts
......256........1600.........10000...........40000...........160000
.....1600.......20000........250000.........1750000.........12250000
....10000......250000.......6250000........76562500........937890625
....40000.....1750000......76562500......1500625000......29412250000
...160000....12250000.....937890625.....29412250000.....922368160000
...490000....60025000....7353062500....345888060000...16270574342400
..1500625...294122500...57648010000...4067643585600..287012931399936
..3841600..1129430400..332052537600..33470895790080.3373866295640064
..9834496..4337012736.1912622616576.275417656786944.................
.22127616.13940398080.8782450790400.................................

/tmp/emd
T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with nondecreasing sum of every three consecutive values in every row and column
Table starts
.....512.....1728.......5832.......19683........46656........110592
....1728.....7776......34992......157464.......466560.......1382400
....5832....34992.....209952.....1259712......4665600......17280000
...19683...157464....1259712....10077696.....46656000.....216000000
...46656...466560....4665600....46656000....259200000....1440000000
..110592..1382400...17280000...216000000...1440000000....9600000000
..262144..4096000...64000000..1000000000...8000000000...64000000000
..512000..9600000..180000000..3375000000..31500000000..294000000000
.1000000.22500000..506250000.11390625000.124031250000.1350562500000
.1953125.52734375.1423828125.38443359375.488373046875..............

/tmp/eme
T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with nondecreasing sum of every three consecutive values in every row and column
Table starts
.......19683.........157464.........1259712..........10077696..........46656000
......157464........2099520........27993600.........373248000........2592000000
.....1259712.......27993600.......622080000.......13824000000......144000000000
....10077696......373248000.....13824000000......512000000000.....8000000000000
....46656000.....2592000000....144000000000.....8000000000000...175000000000000
...216000000....18000000000...1500000000000...125000000000000..3828125000000000
..1000000000...125000000000..15625000000000..1953125000000000.83740234375000000
..3375000000...590625000000.103359375000000.18087890625000000..................
.11390625000..2790703125000.683722265625000....................................
.38443359375.13186072265625....................................................

rhhardin at mindspring.com
rhhardin at att.net (either)

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