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Number of nX2 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
6

%I #4 Jan 19 2018 08:34:05

%S 1,4,4,16,48,88,240,704,1600,4032,11072,27392,68608,180736,459776,

%T 1160704,2999296,7682048,19525632,50081792,128339968,327434240,

%U 837861376,2145583104,5483266048,14023229440,35888758784,91776090112,234707222528

%N Number of nX2 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

%C Column 2 of A298454.

%H R. H. Hardin, <a href="/A298448/b298448.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A298454.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 19 2018