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%I #9 Nov 22 2015 13:19:46
%S 0,0,1,33,413,2859,13976,54199,177848,513905,1342933,3233784,7275049,
%T 15451358,31234528,60485192,112793064,203424686,356097793,606862907,
%U 1009447181,1642504781,2619324320,4100669333,6311574992,9563095895
%N Number of n X 3 nonnegative integer arrays with upper left 0 and lower right n+3-6 and value increasing by 0 or 1 with every step right or down.
%C Column 3 of A252930.
%H R. H. Hardin, <a href="/A252925/b252925.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/59875200)*n^12 + (1/997920)*n^11 + (31/1360800)*n^10 + (1/5040)*n^9 + (79/453600)*n^8 - (71/15120)*n^7 - (4127/1360800)*n^6 + (319/9072)*n^5 + (52061/5443200)*n^4 - (2587/6048)*n^3 + (3315209/1663200)*n^2 - (11097/3080)*n + 2.
%F Empirical: G.f.: -x^3*(1 +20*x +62*x^2 -222*x^3 +300*x^4 -297*x^5 +255*x^6 -167*x^7 +72*x^8 -18*x^9 +2*x^10) / (x-1)^13. - _R. J. Mathar_, Nov 21 2015
%e Some solutions for n=4:
%e ..0..0..0....0..0..0....0..0..1....0..0..0....0..1..1....0..0..0....0..0..0
%e ..0..1..1....0..0..0....0..0..1....0..0..1....1..1..1....0..0..0....0..1..1
%e ..1..1..1....0..1..1....0..1..1....0..0..1....1..1..1....0..0..0....0..1..1
%e ..1..1..1....1..1..1....0..1..1....0..0..1....1..1..1....0..0..1....0..1..1
%K nonn
%O 1,4
%A _R. H. Hardin_, Dec 24 2014
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