%I #4 May 24 2018 08:40:32

%S 4,3,7,7,13,23,37,63,109,183,309,527,893,1511,2565,4351,7373,12503,

%T 21205,35951,60957,103367,175269,297183,503917,854455,1448821,2456655,

%U 4165565,7063207,11976517,20307647,34434061,58387095,99002389,167870511

%N Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A305040.

%H R. H. Hardin, <a href="/A305035/b305035.txt">Table of n, a(n) for n = 1..210</a>

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

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A305040.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 24 2018