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Number of nX2 0..1 arrays with every element unequal to 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.
8

%I #4 May 04 2018 11:27:53

%S 1,7,16,45,120,333,928,2613,7400,21053,60080,171845,492280,1411789,

%T 4051904,11635413,33424648,96042845,276020944,793366629,2280573208,

%U 6556026349,18847591392,54185601013,155783294760,447882509949

%N Number of nX2 0..1 arrays with every element unequal to 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

%C Column 2 of A304019.

%H R. H. Hardin, <a href="/A304013/b304013.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A304019.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 04 2018