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A239531 Number of (n+1) X (2+1) 0..2 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..2 introduced in row major order.

%I A239531 #7 Oct 26 2018 09:14:49
%S A239531 2,2,24,68,406,1584,7790,33630,156032,695344,3168922,14262616,
%T A239531 64640674,291830210,1320357280,5966652996,26981170086,121963213688,
%U A239531 551425857374,2492844327694,11270188295640,50950869428672,230346017497690
%N A239531 Number of (n+1) X (2+1) 0..2 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..2 introduced in row major order.
%H A239531 R. H. Hardin, <a href="/A239531/b239531.txt">Table of n, a(n) for n = 1..210</a>
%F A239531 Empirical: a(n) = 2*a(n-1) + 13*a(n-2) - a(n-3) - 23*a(n-4) - 28*a(n-5) + 11*a(n-6) + 40*a(n-7) - 9*a(n-8) - 5*a(n-9) + 5*a(n-10).
%F A239531 Empirical g.f.: 2*x*(1 - x - 3*x^2 - 2*x^3 + 3*x^4 + 7*x^5 - x^6 - x^7 + x^8) / (1 - 2*x - 13*x^2 + x^3 + 23*x^4 + 28*x^5 - 11*x^6 - 40*x^7 + 9*x^8 + 5*x^9 - 5*x^10). - _Colin Barker_, Oct 26 2018
%e A239531 Some solutions for n=5:
%e A239531 ..0..1..2....0..1..0....0..1..0....0..1..2....0..1..0....0..1..2....0..1..2
%e A239531 ..0..1..2....0..1..0....0..1..0....0..1..2....0..1..0....0..1..2....0..1..2
%e A239531 ..0..1..0....0..1..2....2..0..2....0..2..0....1..2..1....0..1..2....2..1..2
%e A239531 ..2..1..0....0..1..2....2..0..2....0..2..0....1..2..1....0..1..2....2..1..2
%e A239531 ..2..1..0....1..2..0....1..0..1....1..0..1....0..1..0....1..0..1....1..2..0
%e A239531 ..2..1..0....1..2..0....1..0..1....1..0..1....0..1..0....1..0..1....1..2..0
%Y A239531 Column 2 of A239537.
%K A239531 nonn
%O A239531 1,1
%A A239531 _R. H. Hardin_, Mar 21 2014