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Number of nX3 0..1 arrays with every element equal to 0, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
1

%I #4 Feb 13 2018 11:22:23

%S 1,1,10,10,27,63,115,267,569,1193,2587,5521,11791,25273,54049,115633,

%T 247475,529485,1132947,2424265,5187219,11099285,23749619,50817867,

%U 108736971,232668795,497850429,1065270295,2279401223,4877325533

%N Number of nX3 0..1 arrays with every element equal to 0, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A299581.

%H R. H. Hardin, <a href="/A299576/b299576.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -4*a(n-4) -2*a(n-5) -2*a(n-6) +a(n-9) for n>13

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A299581.

%K nonn

%O 1,3

%A _R. H. Hardin_, Feb 13 2018