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Number of n X 3 0..1 arrays with every element unequal to 0, 1, 2, 3 or 7 king-move adjacent elements, with upper left element zero.
1

%I #6 Dec 28 2023 23:21:20

%S 4,21,27,67,139,303,685,1511,3316,7349,16265,35899,79332,175408,

%T 387618,856555,1893162,4184055,9246710,20435743,45164387,99815208,

%U 220596189,487529334,1077464178,2381248108,5262677458,11630780579,25704601383

%N Number of n X 3 0..1 arrays with every element unequal to 0, 1, 2, 3 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A304775.

%H R. H. Hardin, <a href="/A304770/b304770.txt">Table of n, a(n) for n = 1..210</a>

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

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A304775.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 18 2018