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Number of n X 2 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 3 1s.
4

%I #8 Feb 21 2018 14:39:26

%S 2,5,11,24,55,123,276,621,1395,3134,7043,15825,35558,79899,179531,

%T 403402,906437,2036745,4576524,10283357,23106493,51919818,116662773,

%U 262138871,589020696,1323517491,2973916807,6682330408,15015060133,33738533867

%N Number of n X 2 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 3 1s.

%C Column 2 of A295097.

%H R. H. Hardin, <a href="/A295091/b295091.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(2 + 3*x + 2*x^2 - x^3 - x^4) / ((1 + x + x^2)*(1 - 2*x - x^2 + x^3)). - _Colin Barker_, Feb 21 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A295097.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 14 2017