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%I #6 Nov 22 2023 21:35:30
%S 1,13,31,156,614,2800,13379,63697,313055,1541446,7631089,37907371,
%T 188460970,938008699,4670538813,23261346000,115871179617,577226703607,
%U 2875668407886,14326569827639,71375895052167,355602303531952
%N Number of n X 3 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Column 3 of A299893.
%H R. H. Hardin, <a href="/A299888/b299888.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) +2*a(n-2) -33*a(n-3) -40*a(n-4) +152*a(n-5) +18*a(n-6) -368*a(n-7) +310*a(n-8) +492*a(n-9) -362*a(n-10) -290*a(n-11) -8*a(n-12) -12*a(n-13) for n>15.
%e Some solutions for n=5
%e ..0..0..0. .0..1..1. .0..0..0. .0..1..0. .0..0..0. .0..0..1. .0..0..0
%e ..0..0..0. .1..1..1. .0..0..1. .0..0..0. .0..1..0. .0..0..0. .0..0..0
%e ..0..0..1. .1..1..1. .0..1..1. .0..0..0. .0..1..1. .0..1..1. .1..1..1
%e ..0..0..0. .1..1..0. .0..0..1. .1..0..0. .0..0..1. .0..1..1. .1..1..1
%e ..0..0..0. .1..1..1. .1..0..0. .0..0..0. .0..1..1. .0..0..1. .1..1..1
%Y Cf. A299893.
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 21 2018
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