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A202808 Number of n X 4 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

%I A202808 #11 Mar 03 2018 05:35:29
%S A202808 1,10,121,1177,8232,43483,185051,666610,2105474,5980085,15560519,
%T A202808 37618385,85418437,183739050,377000959,742024924,1407514167,
%U A202808 2583094972,4601680965,7980089529,13504273038,22347278077,36230162235,57638635054
%N A202808 Number of n X 4 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.
%C A202808 Column 4 of A202812.
%H A202808 R. H. Hardin, <a href="/A202808/b202808.txt">Table of n, a(n) for n = 1..210</a>
%F A202808 Empirical: a(n) = (59/119750400)*n^12 + (59/3991680)*n^11 + (157/777600)*n^10 + (1033/725760)*n^9 + (18839/3628800)*n^8 + (289/60480)*n^7 - (11717/1360800)*n^6 + (38509/725760)*n^5 + (129613/388800)*n^4 + (1511/181440)*n^3 - (274553/831600)*n^2 + (12923/13860)*n.
%F A202808 Conjectures from _Colin Barker_, Mar 03 2018: (Start)
%F A202808 G.f.: x*(1 - 3*x + 69*x^2 + 98*x^3 + 224*x^4 - 470*x^5 + 607*x^6 - 459*x^7 + 228*x^8 - 71*x^9 + 13*x^10 - x^11) / (1 - x)^13.
%F A202808 a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n>13.
%F A202808 (End)
%e A202808 Some solutions for n=5:
%e A202808   0 0 0 0    0 0 0 0    0 0 0 0    0 0 0 0    0 0 0 0
%e A202808   0 0 2 2    0 0 2 2    0 0 0 2    0 0 1 2    0 0 0 1
%e A202808   0 2 2 4    0 0 2 3    0 1 1 3    0 0 1 2    0 1 1 3
%e A202808   0 2 3 4    0 1 3 5    0 1 2 3    0 1 1 3    0 1 3 3
%e A202808   0 2 3 4    0 2 4 5    0 2 2 4    0 2 3 4    0 1 3 3
%Y A202808 Cf. A202812.
%K A202808 nonn
%O A202808 1,2
%A A202808 _R. H. Hardin_, Dec 24 2011