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%I #6 Nov 17 2022 18:19:59
%S 0,3,9,21,127,513,2440,11458,53727,254534,1202650,5692243,26943691,
%T 127540324,603796896,2858444154,13532486972,64065914939,303303284790,
%U 1435912281177,6797962755503,32183241315912,152363457753491
%N Number of n X 3 0..1 arrays with every element equal to 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Column 3 of A298841.
%H R. H. Hardin, <a href="/A298836/b298836.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) +6*a(n-2) -31*a(n-3) -40*a(n-4) +100*a(n-5) +105*a(n-6) -167*a(n-7) -101*a(n-8) +118*a(n-9) +29*a(n-10) -19*a(n-11) +4*a(n-12) for n>14.
%e Some solutions for n=7
%e ..0..0..0. .0..0..0. .0..1..1. .0..0..0. .0..0..0. .0..0..0. .0..0..0
%e ..0..0..0. .0..0..0. .0..0..1. .0..0..0. .0..0..0. .0..1..0. .0..0..0
%e ..0..0..0. .0..0..0. .1..0..1. .0..0..0. .1..1..1. .1..1..1. .0..0..0
%e ..1..1..1. .0..0..0. .1..1..1. .1..1..1. .1..1..1. .0..0..0. .1..1..1
%e ..1..0..1. .0..0..0. .0..0..0. .1..1..0. .1..1..1. .0..0..0. .0..1..1
%e ..0..1..0. .1..1..1. .0..0..0. .1..0..0. .1..1..1. .0..0..0. .0..0..1
%e ..0..0..0. .1..1..1. .0..0..0. .1..1..0. .1..1..1. .0..0..0. .0..0..0
%Y Cf. A298841.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 27 2018
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