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Number of n X 2 0..1 arrays with every element equal to 0, 1, 3 or 4 king-move adjacent elements, with upper left element zero.
6

%I #7 Feb 19 2018 14:13:38

%S 2,4,3,13,34,73,203,594,1443,4013,11114,29073,79243,216234,577883,

%T 1566413,4247794,11437273,30940683,83723074,225989523,610970413,

%U 1651964474,4462848673,12062978123,32607525914,88115865163,238159441613

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

%C Column 2 of A297907.

%H R. H. Hardin, <a href="/A297901/b297901.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 3*a(n-2) + 8*a(n-3) - 4*a(n-4) - 16*a(n-5) for n>6.

%F Empirical g.f.: x*(1 + 2*x)*(2 - 2*x - 3*x^2 - 12*x^3 + 12*x^4) / (1 - x - 3*x^2 - 8*x^3 + 4*x^4 + 16*x^5). - _Colin Barker_, Feb 19 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Cf. A297907.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2018