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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) or (1,0), with upper left element zero.
1

%I #8 Feb 07 2019 08:42:07

%S 0,2,3,10,27,76,214,599,1683,4721,13250,37183,104346,292828,821761,

%T 2306111,6471639,18161366,50966255,143026636,401375754,1126381063,

%U 3160963987,8870615501,24893614638,69858968603,196045273658,550161991984

%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) or (1,0), with upper left element zero.

%H R. H. Hardin, <a href="/A278088/b278088.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x^2*(2 + x - x^2 - x^3) / (1 - x - 4*x^2 - 3*x^3). - _Colin Barker_, Feb 07 2019

%e All solutions for n=4:

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

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

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

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

%Y Column 2 of A278094.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 11 2016