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Number of nX3 0..1 arrays with each 1 adjacent to 3, 4 or 5 king-move neighboring 1s.
1

%I #4 Dec 22 2017 18:22:54

%S 1,4,14,28,98,447,1653,6507,27374,111866,455776,1879650,7732294,

%T 31739780,130516126,536728543,2206092839,9069307066,37287485232,

%U 153290332616,630187059733,2590803232685,10651107068004,43787867995065

%N Number of nX3 0..1 arrays with each 1 adjacent to 3, 4 or 5 king-move neighboring 1s.

%C Column 3 of A296990.

%H R. H. Hardin, <a href="/A296985/b296985.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +2*a(n-2) +19*a(n-3) -19*a(n-4) -52*a(n-5) -67*a(n-6) +15*a(n-7) +155*a(n-8) +207*a(n-9) -104*a(n-10) -157*a(n-11) -172*a(n-12) +53*a(n-13) +63*a(n-14) +38*a(n-15) +14*a(n-16) +19*a(n-17) +3*a(n-18) +4*a(n-19) +2*a(n-20)

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A296990.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 22 2017