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Number of nX3 0..1 arrays with every element equal to 0, 1, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
1

%I #6 Feb 25 2018 06:16:50

%S 3,4,1,4,10,6,19,41,32,106,177,204,567,854,1301,3067,4579,8193,16931,

%T 26544,50620,96460,160794,309917,567494,993732,1895366,3426279,

%U 6187957,11638394,21056192,38635839,71892662,130796451,241549120,446677807

%N Number of nX3 0..1 arrays with every element equal to 0, 1, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A300089.

%H R. H. Hardin, <a href="/A300084/b300084.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -10*a(n-4) +2*a(n-5) +2*a(n-6) +2*a(n-7) -3*a(n-8) -3*a(n-9) +12*a(n-10) -4*a(n-11) +17*a(n-12) -3*a(n-13) -5*a(n-14) +a(n-15) -12*a(n-16) -6*a(n-17) -2*a(n-18) -3*a(n-19) -a(n-20) for n>21

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A300089.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 24 2018