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A229423 Number of n X 3 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.

%I A229423 #8 Sep 15 2018 08:44:33
%S A229423 8,27,83,222,524,1116,2187,4005,6936,11465,18219,27992,41772,60770,
%T A229423 86451,120567,165192,222759,296099,388482,503660,645912,820091,
%U A229423 1031673,1286808,1592373,1956027,2386268,2892492,3485054,4175331,4975787,5900040,6962931
%N A229423 Number of n X 3 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.
%H A229423 R. H. Hardin, <a href="/A229423/b229423.txt">Table of n, a(n) for n = 1..210</a>
%F A229423 Empirical: a(n) = (1/360)*n^6 + (1/20)*n^5 + (5/18)*n^4 + (2/3)*n^3 + (799/360)*n^2 + (107/60)*n + 3.
%F A229423 Conjectures from _Colin Barker_, Sep 15 2018: (Start)
%F A229423 G.f.: x*(8 - 29*x + 62*x^2 - 72*x^3 + 48*x^4 - 18*x^5 + 3*x^6) / (1 - x)^7.
%F A229423 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 A229423 (End)
%e A229423 Some solutions for n=4:
%e A229423 ..1..0..0....1..1..0....0..0..0....1..1..1....1..0..0....0..0..0....1..0..0
%e A229423 ..2..1..1....2..1..0....1..1..0....1..1..1....2..1..1....1..1..0....2..1..0
%e A229423 ..2..1..1....2..2..1....1..1..1....1..1..1....2..2..1....1..1..0....2..1..1
%e A229423 ..2..2..1....2..2..1....1..1..1....1..1..1....2..2..2....1..1..1....2..2..2
%Y A229423 Column 3 of A229428.
%K A229423 nonn
%O A229423 1,1
%A A229423 _R. H. Hardin_, Sep 22 2013