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Number of nX2 n X 2 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

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

Empirical g.f.: x*(2 + 6*x + 5*x^2 - x^3 - 2*x^4 - x^5) / (1 - 2*x - 2*x^2 - 5*x^3 + x^5 + x^6). - Colin Barker, Feb 21 2018

Some solutions for n=5:

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R. H. Hardin, <a href="/A295525/b295525.txt">Table of n, a(n) for n = 1..210</a>

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Number of nX2 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

2, 10, 29, 87, 280, 876, 2735, 8583, 26900, 84274, 264107, 827651, 2593568, 8127490, 25469197, 79812833, 250109752, 783769936, 2456102483, 7696696911, 24119166438, 75582316528, 236852570799, 742225734425, 2325915393694, 7288729246884

1,1

Column 2 of A295531.

Empirical: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)

Some solutions for n=5

..1..1. .1..1. .1..1. .1..1. .1..0. .0..0. .0..0. .0..0. .0..1. .1..1

..1..0. .1..0. .1..1. .0..0. .1..0. .1..1. .1..1. .1..1. .0..1. .0..1

..1..1. .0..0. .0..0. .1..1. .1..0. .1..0. .0..0. .0..0. .0..0. .0..1

..0..1. .0..1. .1..0. .0..1. .1..1. .1..0. .1..1. .1..1. .1..0. .0..0

..0..1. .1..1. .1..1. .0..1. .0..0. .0..0. .1..0. .1..1. .1..1. .1..1

Cf. A295531.

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R. H. Hardin, Nov 23 2017

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