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%I #6 Sep 03 2022 22:36:52
%S 4,21,42,125,361,987,2840,8177,23078,66092,189934,542549,1555968,
%T 4472084,12834117,36874076,106057815,304978090,877344581,2525161569,
%U 7268401508,20925202372,60256501068,173532468268,499807464421,1439715507607
%N Number of n X 3 0..1 arrays with every element unequal to 0, 1, 2, 3, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Column 3 of A316289.
%H R. H. Hardin, <a href="/A316284/b316284.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +a(n-2) +6*a(n-3) -23*a(n-4) -22*a(n-5) +7*a(n-6) +27*a(n-7) +24*a(n-8) -18*a(n-9) -10*a(n-10) for n>12.
%e Some solutions for n=5
%e ..0..1..1. .0..1..0. .0..1..1. .0..1..0. .0..0..0. .0..1..0. .0..1..0
%e ..0..1..1. .1..0..1. .0..1..0. .1..0..1. .0..0..0. .1..1..1. .0..1..1
%e ..1..0..1. .1..1..1. .0..0..0. .1..1..1. .1..1..1. .1..1..1. .0..0..0
%e ..1..0..1. .1..1..1. .0..0..0. .0..0..1. .1..1..1. .0..0..1. .0..1..0
%e ..0..1..1. .1..1..0. .1..0..1. .1..0..1. .0..1..0. .0..1..1. .0..0..0
%Y Cf. A316289.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 28 2018