%I #7 Sep 30 2023 16:37:45
%S 3,7,10,17,32,56,93,159,279,484,829,1426,2468,4265,7349,12669,21870,
%T 37749,65116,112324,193813,334427,576983,995444,1717497,2963334,
%U 5112744,8821129,15219457,26258869,45305486,78167201,134864984,232688208
%N Number of n X 3 0..1 arrays with every element unequal to 0, 1, 3 or 8 king-move adjacent elements, with upper left element zero.
%C Column 3 of A304221.
%H R. H. Hardin, <a href="/A304216/b304216.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) +a(n-3) +2*a(n-4) for n>5.
%e Some solutions for n=7:
%e ..0..0..0. .0..0..0. .0..0..0. .0..0..1. .0..0..0. .0..0..1. .0..1..1
%e ..0..0..0. .0..1..0. .0..1..0. .0..1..1. .0..0..0. .0..1..1. .0..0..1
%e ..0..0..0. .0..0..0. .0..0..0. .1..1..1. .0..0..0. .1..1..1. .0..0..0
%e ..0..0..0. .0..0..0. .0..0..0. .1..1..1. .0..1..0. .1..1..1. .0..0..0
%e ..0..0..1. .0..0..0. .0..0..0. .1..0..1. .0..0..0. .1..1..1. .0..0..1
%e ..0..1..1. .0..0..0. .0..0..1. .1..1..1. .0..0..0. .0..1..1. .0..1..1
%e ..1..1..1. .0..0..0. .0..1..1. .1..1..1. .1..0..0. .0..0..1. .1..1..1
%Y Cf. A304221.
%K nonn
%O 1,1
%A _R. H. Hardin_, May 08 2018