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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.
1

%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