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A229450 Number of 7 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 A229450 #7 Sep 17 2018 08:32:13
%S A229450 30,142,625,2402,8024,23610,62205,149031,329106,677706,1314145,
%T A229450 2419348,4257692,7203590,11773293,18662385,28789446,43346358,63855729,
%U A229450 92235910,130874080,182707874,251316029,341018523,456986682,605363730,793396257
%N A229450 Number of 7 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 A229450 R. H. Hardin, <a href="/A229450/b229450.txt">Table of n, a(n) for n = 1..210</a>
%F A229450 Empirical: a(n) = (95/1008)*n^7 - (241/360)*n^6 + (232/45)*n^5 - (1061/72)*n^4 + (5771/144)*n^3 - (7217/180)*n^2 + (18133/420)*n - 3.
%F A229450 Conjectures from _Colin Barker_, Sep 17 2018: (Start)
%F A229450 G.f.: x*(30 - 98*x + 329*x^2 - 302*x^3 + 456*x^4 - 66*x^5 + 123*x^6 + 3*x^7) / (1 - x)^8.
%F A229450 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F A229450 (End)
%e A229450 Some solutions for n=4:
%e A229450 ..0..2..2..2....0..2..2..2....0..2..2..2....0..2..2..2....0..0..2..2
%e A229450 ..1..0..2..2....1..0..0..2....1..0..0..2....0..2..2..2....0..0..2..2
%e A229450 ..1..0..2..2....1..1..1..0....1..0..0..2....0..2..2..2....1..1..0..0
%e A229450 ..1..1..0..0....2..2..2..1....2..1..1..0....0..2..2..2....1..1..1..1
%e A229450 ..1..1..1..1....2..2..2..2....2..2..2..1....1..0..0..2....1..1..1..1
%e A229450 ..1..1..1..1....2..2..2..2....2..2..2..1....1..1..1..0....1..1..1..1
%e A229450 ..2..2..2..2....2..2..2..2....2..2..2..2....1..1..1..1....1..1..1..1
%Y A229450 Row 7 of A229445.
%K A229450 nonn
%O A229450 1,1
%A A229450 _R. H. Hardin_, Sep 23 2013