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Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3 or 8 king-move adjacent elements, with upper left element zero.
1

%I #4 May 27 2018 17:42:04

%S 4,21,24,54,108,236,509,1091,2363,5109,11034,23867,51606,111571,

%T 241263,521680,1128006,2439107,5274072,11404090,24659080,53320283,

%U 115294335,249300825,539062799,1165614674,2520407019,5449872468,11784251403

%N Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A305230.

%H R. H. Hardin, <a href="/A305225/b305225.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +a(n-2) -3*a(n-4) -a(n-5) +2*a(n-6) for n>9

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A305230.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 27 2018