cp's OEIS Frontend

A202754 Number of n X 6 nonnegative integer arrays with each row and column increasing from zero by 0 or 1.

%I A202754 #10 Jun 02 2019 23:38:23
%S A202754 1,6,51,462,3809,26394,150777,721382,2964632,10720688,34811491,
%T A202754 103179440,282848319,724794396,1751160378,4017593748,8804203831,
%U A202754 18519925138,37551252015,73653037370,140173677721,259538952486,468599962315
%N A202754 Number of n X 6 nonnegative integer arrays with each row and column increasing from zero by 0 or 1.
%C A202754 Column 6 of A202756.
%H A202754 R. H. Hardin, <a href="/A202754/b202754.txt">Table of n, a(n) for n = 1..210</a>
%H A202754 Robert Israel, <a href="/A202754/a202754.pdf">Maple-assisted proof of empirical formula</a>
%F A202754 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.
%F A202754 Empirical formula verified (see link). - _Robert Israel_, Jun 02 2019
%e A202754 Some solutions for n=5:
%e A202754   0 0 0 0 0 0   0 0 0 0 0 0   0 0 0 0 0 0   0 0 0 0 0 0
%e A202754   0 0 1 1 1 1   0 0 0 1 1 1   0 0 0 0 0 0   0 0 0 1 1 1
%e A202754   0 0 1 1 2 2   0 0 0 1 2 2   0 0 0 0 1 1   0 0 0 1 1 2
%e A202754   0 0 1 1 2 2   0 0 0 1 2 3   0 0 1 1 1 2   0 0 1 2 2 3
%e A202754   0 1 2 2 2 2   0 0 1 2 3 3   0 1 2 2 2 3   0 1 2 3 3 4
%p A202754 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
%K A202754 nonn
%O A202754 1,2
%A A202754 _R. H. Hardin_, Dec 23 2011