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

%I #4 May 10 2018 08:59:27

%S 1,2,3,5,6,14,22,33,57,97,159,255,432,724,1171,1951,3254,5363,8858,

%T 14694,24381,40260,66642,110538,182870,302621,501272,830095,1374018,

%U 2274695,3767129,6236893,10324974,17096385,28307135,46865638,77594124,128475252

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

%C Column 3 of A304302.

%H R. H. Hardin, <a href="/A304297/b304297.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-2) +3*a(n-3) +2*a(n-4) -4*a(n-6) -2*a(n-7) -a(n-8) -2*a(n-9)

%e All solutions for n=5

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

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

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

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

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

%Y Cf. A304302.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 10 2018