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Number of n X 2 0..1 arrays with every element equal to 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
8

%I #7 Feb 19 2018 14:15:58

%S 0,1,3,6,17,41,104,261,655,1646,4133,10381,26072,65481,164459,413046,

%T 1037385,2605441,6543688,16434781,41276727,103668446,260368189,

%U 653926981,1642368440,4124885761,10359845043,26019239206,65348545857,164125953561

%N Number of n X 2 0..1 arrays with every element equal to 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

%C Column 2 of A297978.

%H R. H. Hardin, <a href="/A297972/b297972.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x^2*(1 + 2*x) / (1 - x - 3*x^2 - 2*x^3). - _Colin Barker_, Feb 19 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Cf. A297978.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jan 10 2018