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%I #4 Jun 23 2018 12:43:15
%S 4,5,17,32,77,207,523,1304,3307,8414,21308,53961,136813,346873,879204,
%T 2228553,5649254,14320348,36300091,92016267,233250975,591264096,
%U 1498784411,3799243014,9630638220,24412541681,61882935885,156866006985
%N Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
%C Column 3 of A306166.
%H R. H. Hardin, <a href="/A306161/b306161.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) +2*a(n-2) +5*a(n-3) +2*a(n-4) -2*a(n-5) -8*a(n-6) -8*a(n-7) for n>10
%e Some solutions for n=5
%e ..0..0..0. .0..1..1. .0..1..0. .0..1..0. .0..1..1. .0..0..0. .0..1..1
%e ..0..0..0. .1..0..1. .0..0..0. .0..0..0. .1..0..1. .1..0..0. .0..1..1
%e ..0..0..0. .1..1..1. .0..1..0. .1..0..0. .1..1..1. .0..0..0. .0..0..0
%e ..0..1..1. .1..1..1. .0..1..0. .0..0..1. .1..1..0. .0..0..0. .0..0..0
%e ..0..1..1. .1..1..1. .0..0..0. .0..0..0. .1..1..1. .0..1..0. .0..0..0
%Y Cf. A306166.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 23 2018
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