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A229446 Number of 3 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 A229446 #8 Sep 17 2018 08:31:48
%S A229446 8,13,22,37,60,93,138,197,272,365,478,613,772,957,1170,1413,1688,1997,
%T A229446 2342,2725,3148,3613,4122,4677,5280,5933,6638,7397,8212,9085,10018,
%U A229446 11013,12072,13197,14390,15653,16988,18397,19882,21445,23088,24813,26622,28517
%N A229446 Number of 3 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 A229446 R. H. Hardin, <a href="/A229446/b229446.txt">Table of n, a(n) for n = 1..210</a>
%F A229446 Empirical: a(n) = (1/3)*n^3 + (8/3)*n + 5.
%F A229446 Conjectures from _Colin Barker_, Sep 17 2018: (Start)
%F A229446 G.f.: x*(8 - 19*x + 18*x^2 - 5*x^3) / (1 - x)^4.
%F A229446 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A229446 (End)
%e A229446 Some solutions for n=4:
%e A229446 ..0..2..2..2....0..0..2..2....0..2..2..2....0..0..0..2....0..0..0..2
%e A229446 ..1..0..2..2....0..0..2..2....1..0..2..2....1..1..1..0....0..0..0..2
%e A229446 ..2..1..0..2....1..1..0..2....2..1..0..0....1..1..1..1....0..0..0..2
%Y A229446 Row 3 of A229445.
%K A229446 nonn
%O A229446 1,1
%A A229446 _R. H. Hardin_, Sep 23 2013