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

%I #4 Feb 16 2018 07:33:08

%S 4,13,20,45,147,506,1561,5017,16429,53365,172859,562276,1828820,

%T 5943264,19318649,62811656,204197935,663816782,2158064264,7015860029,

%U 22808258862,74148897744,241056311862,783667226084,2547678766746,8282432122501

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

%C Column 3 of A299682.

%H R. H. Hardin, <a href="/A299677/b299677.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3) -16*a(n-4) -13*a(n-5) +12*a(n-6) +40*a(n-7) +23*a(n-8) -37*a(n-9) +15*a(n-10) -88*a(n-11) +52*a(n-12) -48*a(n-13) +49*a(n-14) -8*a(n-15) +20*a(n-16) for n>17

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A299682.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 16 2018