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Number of n X 2 0..1 arrays with each 1 adjacent to 1 or 3 king-move neighboring 1s.
1

%I #8 Feb 22 2019 11:08:42

%S 2,8,15,33,104,228,529,1469,3442,8212,21431,51717,125296,317400,

%T 775809,1895433,4734066,11634128,28553071,70839225,174478216,

%U 429240572,1061586753,2617025573,6446295426,15919369724,39257673143,96762290109

%N Number of n X 2 0..1 arrays with each 1 adjacent to 1 or 3 king-move neighboring 1s.

%H R. H. Hardin, <a href="/A295937/b295937.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + a(n-2) + 9*a(n-3) - 4*a(n-4) - 4*a(n-5) - 4*a(n-6).

%F Empirical g.f.: x*(2 + 6*x + 5*x^2 - 8*x^3 - 8*x^4 - 4*x^5) / (1 - x - x^2 - 9*x^3 + 4*x^4 + 4*x^5 + 4*x^6). - _Colin Barker_, Feb 22 2019

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 2 of A295943.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 30 2017