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Number of nX3 0..1 arrays with every element equal to 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
1

%I #4 Feb 07 2018 04:47:20

%S 0,3,8,36,173,858,4258,21386,107465,541047,2725498,13733762,69215100,

%T 348852964,1758324488,8862635135,44671460074,225164071583,

%U 1134929377517,5720565544510,28834291127949,145338167739511,732571679461791

%N Number of nX3 0..1 arrays with every element equal to 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A299334.

%H R. H. Hardin, <a href="/A299329/b299329.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +10*a(n-2) -13*a(n-3) -53*a(n-4) -25*a(n-5) +57*a(n-6) +53*a(n-7) +a(n-8) +16*a(n-9) +10*a(n-10) -15*a(n-11) -4*a(n-12) for n>14

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A299334.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 07 2018