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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,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) or (1,0), with upper left element zero.
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%I #7 Feb 07 2019 08:55:59

%S 0,2,7,22,75,254,859,2906,9831,33258,112511,380622,1287635,4356038,

%T 14736371,49852786,168650767,570541458,1930127927,6529576006,

%U 22089397403,74727896142,252802661835,855225279050,2893206395127,9787647126266

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

%H R. H. Hardin, <a href="/A278151/b278151.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x^2*(2 - x)*(1 + x) / (1 - 3*x - x^2 - x^3). - _Colin Barker_, Feb 07 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A278157.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 13 2016