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A241125 Number of n X 2 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.

%I A241125 #9 Oct 29 2018 20:16:25
%S A241125 2,9,54,325,1965,11876,71793,434007,2623694,15861001,95884409,
%T A241125 579649484,3504151829,21183629803,128061281038,774168159805,
%U A241125 4680074530261,28292428888436,171036065180937,1033963386740399,6250613190784174
%N A241125 Number of n X 2 0..2 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..2 introduced in row major order.
%H A241125 R. H. Hardin, <a href="/A241125/b241125.txt">Table of n, a(n) for n = 1..210</a>
%F A241125 Empirical: a(n) = 6*a(n-1) + 2*a(n-2) -  9*a(n-3) - 10*a(n-4) + 8*a(n-5) for n>6.
%F A241125 Empirical g.f.: x*(1 - x)*(1 - 2*x)*(2 + 3*x + x^2 - 2*x^3) / (1 - 6*x - 2*x^2 + 9*x^3 + 10*x^4 - 8*x^5). - _Colin Barker_, Oct 29 2018
%e A241125 Some solutions for n=4:
%e A241125 ..0..1....0..1....0..0....0..1....0..1....0..1....0..1....0..1....0..0....0..1
%e A241125 ..1..2....0..1....1..2....2..0....0..2....1..0....1..0....1..2....1..2....0..1
%e A241125 ..2..0....1..2....0..1....0..1....1..1....0..1....1..2....1..0....0..2....1..0
%e A241125 ..1..1....2..0....1..2....0..1....2..2....0..2....2..0....0..1....0..1....1..0
%Y A241125 Column 2 of A241130.
%K A241125 nonn
%O A241125 1,1
%A A241125 _R. H. Hardin_, Apr 16 2014