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A251144 Number of (n+1) X (3+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.

%I A251144 #16 Nov 26 2018 11:23:52
%S A251144 53,87,143,247,433,777,1413,2607,4863,9167,17433,33417,64493,125207,
%T A251144 244303,478727,941473,1857097,3672373,7277087,14444703,28712287,
%U A251144 57137993,113812297,226874333,452534727,903105263,1803032407,3600922513
%N A251144 Number of (n+1) X (3+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.
%H A251144 R. H. Hardin, <a href="/A251144/b251144.txt">Table of n, a(n) for n = 1..210</a>
%F A251144 Empirical: a(n) = 3*a(n-1) - 5*a(n-3) + a(n-4) + 2*a(n-5)..
%F A251144 Empirical g.f.: x*(53 - 72*x - 118*x^2 + 83*x^3 + 74*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - _Colin Barker_, Nov 26 2018
%e A251144 Some solutions for n=4:
%e A251144 ..2..1..1..0....0..1..1..1....1..1..1..1....1..0..2..1....0..1..0..1
%e A251144 ..1..0..2..1....1..2..0..2....1..1..1..1....2..1..1..0....2..1..2..1
%e A251144 ..2..1..1..0....0..1..1..1....2..0..2..0....0..1..1..2....0..1..0..1
%e A251144 ..1..0..2..1....2..1..1..1....1..1..1..1....1..2..0..1....1..2..1..2
%e A251144 ..2..1..1..0....0..1..1..1....1..1..1..1....0..1..1..2....0..1..0..1
%Y A251144 Column 3 of A251149.
%K A251144 nonn
%O A251144 1,1
%A A251144 _R. H. Hardin_, Nov 30 2014