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Number of n X 2 0..1 arrays with every element both equal and not equal to some elements at offset (-1,0) (-1,1) (0,-1) (0,1) (1,-1) or (1,0), with upper left element zero.
1

%I #10 Feb 08 2019 12:29:42

%S 0,2,5,13,43,137,436,1394,4458,14258,45607,145888,466673,1492823,

%T 4775347,15275728,48865129,156313412,500027005,1599523726,5116675993,

%U 16367605483,52357919474,167486425305,535768092953,1713855012003,5482407483581

%N Number of n X 2 0..1 arrays with every element both equal and not equal to some elements at offset (-1,0) (-1,1) (0,-1) (0,1) (1,-1) or (1,0), with upper left element zero.

%H R. H. Hardin, <a href="/A278171/b278171.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + a(n-2) - 3*a(n-4) - 2*a(n-5) - a(n-6) for n>7.

%F Empirical g.f.: x^2*(1 + x)*(2 - 3*x - x^2 + x^4) / (1 - 3*x - x^2 + 3*x^4 + 2*x^5 + x^6). - _Colin Barker_, Feb 08 2019

%e Some solutions for n=4:

%e ..0..1. .0..1. .0..1. .0..0. .0..1. .0..0. .0..1. .0..0. .0..0. .0..0

%e ..0..1. .0..1. .0..1. .1..1. .0..1. .1..1. .0..1. .1..1. .1..0. .1..1

%e ..0..1. .1..1. .1..0. .0..0. .0..0. .1..0. .0..1. .0..1. .1..0. .1..1

%e ..0..0. .0..0. .1..0. .1..1. .1..1. .1..0. .0..1. .0..1. .1..1. .0..0

%Y Column 2 of A278177.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 13 2016