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

%I #4 Jan 08 2018 08:09:18

%S 1,17,109,588,3276,18451,103558,581318,3263838,18323588,102871721,

%T 577541657,3242423256,18203555673,102198092227,573758755891,

%U 3221186481709,18084329459118,101528729659838,570000838170243

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

%C Column 3 of A297923.

%H R. H. Hardin, <a href="/A297918/b297918.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +3*a(n-2) +6*a(n-3) -17*a(n-4) -12*a(n-5) -7*a(n-6) -36*a(n-7) +6*a(n-8) -19*a(n-9) for n>12

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A297923.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 08 2018