%I
%S 12,25,53,109,212,387,665,1083,1684,2517,3637,5105,6988,9359,12297,
%T 15887,20220,25393,31509,38677,47012,56635,67673,80259,94532,110637,
%U 128725,148953,171484,196487,224137,254615,288108,324809,364917,408637,456180
%N 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 R. H. Hardin, <a href="/A229447/b229447.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/4)*n^4  (1/3)*n^3 + (13/4)*n^2 + (11/6)*n + 7.
%F Conjectures from _Colin Barker_, Sep 17 2018: (Start)
%F G.f.: x*(12  35*x + 48*x^2  26*x^3 + 7*x^4) / (1  x)^5.
%F a(n) = 5*a(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5) for n>5.
%F (End)
%e Some solutions for n=4:
%e ..0..0..0..2....0..0..0..2....0..0..0..2....0..2..2..2....0..0..0..0
%e ..1..1..1..0....1..1..1..0....1..1..1..0....1..0..2..2....1..1..1..1
%e ..2..2..2..1....1..1..1..0....1..1..1..1....1..0..2..2....2..2..2..2
%e ..2..2..2..2....2..2..2..1....2..2..2..1....2..1..0..2....2..2..2..2
%Y Row 4 of A229445.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 23 2013
