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A229447 Number of 4 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

%I A229447 #8 Sep 17 2018 08:31:54
%S A229447 12,25,53,109,212,387,665,1083,1684,2517,3637,5105,6988,9359,12297,
%T A229447 15887,20220,25393,31509,38677,47012,56635,67673,80259,94532,110637,
%U A229447 128725,148953,171484,196487,224137,254615,288108,324809,364917,408637,456180
%N A229447 Number of 4 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
%H A229447 R. H. Hardin, <a href="/A229447/b229447.txt">Table of n, a(n) for n = 1..210</a>
%F A229447 Empirical: a(n) = (1/4)*n^4 - (1/3)*n^3 + (13/4)*n^2 + (11/6)*n + 7.
%F A229447 Conjectures from _Colin Barker_, Sep 17 2018: (Start)
%F A229447 G.f.: x*(12 - 35*x + 48*x^2 - 26*x^3 + 7*x^4) / (1 - x)^5.
%F A229447 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A229447 (End)
%e A229447 Some solutions for n=4:
%e A229447 ..0..0..0..2....0..0..0..2....0..0..0..2....0..2..2..2....0..0..0..0
%e A229447 ..1..1..1..0....1..1..1..0....1..1..1..0....1..0..2..2....1..1..1..1
%e A229447 ..2..2..2..1....1..1..1..0....1..1..1..1....1..0..2..2....2..2..2..2
%e A229447 ..2..2..2..2....2..2..2..1....2..2..2..1....2..1..0..2....2..2..2..2
%Y A229447 Row 4 of A229445.
%K A229447 nonn
%O A229447 1,1
%A A229447 _R. H. Hardin_, Sep 23 2013