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A229440 Number of n X 3 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

%I A229440 #8 Sep 17 2018 08:31:23
%S A229440 5,10,22,53,128,293,625,1244,2327,4124,6976,11335,17786,27071,40115,
%T A229440 58054,82265,114398,156410,210601,279652,366665,475205,609344,773707,
%U A229440 973520,1214660,1503707,1847998,2255683,2735783,3298250,3954029,4715122
%N A229440 Number of n X 3 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
%H A229440 R. H. Hardin, <a href="/A229440/b229440.txt">Table of n, a(n) for n = 1..210</a>
%F A229440 Empirical: a(n) = (1/360)*n^6 + (1/120)*n^5 + (1/36)*n^4 + (5/24)*n^3 - (11/360)*n^2 + (167/60)*n + 2.
%F A229440 Conjectures from _Colin Barker_, Sep 17 2018: (Start)
%F A229440 G.f.: x*(5 - 25*x + 57*x^2 - 66*x^3 + 44*x^4 - 15*x^5 + 2*x^6) / (1 - x)^7.
%F A229440 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A229440 (End)
%e A229440 Some solutions for n=4:
%e A229440 ..0..2..2....0..2..2....0..2..2....0..2..2....0..2..2....0..2..2....0..2..2
%e A229440 ..1..0..2....0..2..2....1..0..2....0..2..2....0..2..2....1..0..0....1..0..2
%e A229440 ..1..0..2....1..0..2....1..0..2....1..0..2....0..2..2....1..1..1....1..1..0
%e A229440 ..1..0..2....2..1..0....1..1..0....1..1..0....1..0..2....2..2..2....1..1..0
%Y A229440 Column 3 of A229445.
%K A229440 nonn
%O A229440 1,1
%A A229440 _R. H. Hardin_, Sep 23 2013