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Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.
1

%I #4 Jun 18 2018 07:36:07

%S 4,21,45,142,439,1261,3826,11770,35152,106027,323339,977445,2953775,

%T 8969080,27186554,82305975,249564286,756677843,2292774262,6949799639,

%U 21069414963,63860628612,193568100369,586780928193,1778655998433

%N Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A306053.

%H R. H. Hardin, <a href="/A306048/b306048.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +9*a(n-3) -20*a(n-4) -27*a(n-5) +11*a(n-6) +33*a(n-7) +18*a(n-8) -22*a(n-9) -10*a(n-10) for n>12

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A306053.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 18 2018