A202754 Number of n X 6 nonnegative integer arrays with each row and column increasing from zero by 0 or 1.
1, 6, 51, 462, 3809, 26394, 150777, 721382, 2964632, 10720688, 34811491, 103179440, 282848319, 724794396, 1751160378, 4017593748, 8804203831, 18519925138, 37551252015, 73653037370, 140173677721, 259538952486, 468599962315
Offset: 1
Keywords
Examples
Some solutions for n=5: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 2 2 0 0 0 1 2 2 0 0 0 0 1 1 0 0 0 1 1 2 0 0 1 1 2 2 0 0 0 1 2 3 0 0 1 1 1 2 0 0 1 2 2 3 0 1 2 2 2 2 0 0 1 2 3 3 0 1 2 2 2 3 0 1 2 3 3 4
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
- Robert Israel, Maple-assisted proof of empirical formula
Programs
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Maple
seq((1/4572288000)*n^15 + (1/76204800)*n^14 + (41/130636800)*n^13 + (1/272160)*n^12 + (12631/653184000)*n^11 + (113/5443200)*n^10 + (2941/914457600)*n^9 + (661/381024)*n^8 + (1820467/326592000)*n^7 - (38281/10886400)*n^6 + (995867/16329600)*n^5 + (4181/68040)*n^4 - (253877/2646000)*n^3 + (233011/529200)*n^2 + (667/1260)*n, n=1..30); # Robert Israel, Jun 02 2019
Formula
Empirical: a(n) = (1/4572288000)*n^15 + (1/76204800)*n^14 + (41/130636800)*n^13 + (1/272160)*n^12 + (12631/653184000)*n^11 + (113/5443200)*n^10 + (2941/914457600)*n^9 + (661/381024)*n^8 + (1820467/326592000)*n^7 - (38281/10886400)*n^6 + (995867/16329600)*n^5 + (4181/68040)*n^4 - (253877/2646000)*n^3 + (233011/529200)*n^2 + (667/1260)*n.
Empirical formula verified (see link). - Robert Israel, Jun 02 2019
Comments