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Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
1

%I #4 Jul 02 2018 09:03:40

%S 4,5,14,27,66,180,484,1261,3346,8912,23666,62840,166959,443676,

%T 1178829,3132091,8322214,22112722,58754687,156114566,414806153,

%U 1102165608,2928521067,7781259792,20675285518,54935502703,145967000962,387843280136

%N Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A316420.

%H R. H. Hardin, <a href="/A316415/b316415.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +3*a(n-2) +4*a(n-3) +2*a(n-4) -3*a(n-5) -9*a(n-6) -6*a(n-7) for n>10

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A316420.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 02 2018