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%I
%S 4,14,29,78,255,743,2197,6663,20052,60193,181342,546463,1645639,
%T 4957325,14936474,45001409,135584151,408514453,1230861778,3708615800,
%U 11174194280,33668360081,101444455039,305657427545,920962321425,2774910487762
%N Number of n X 3 0..1 arrays with every element unequal to 0, 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
%C Column 3 of A305642.
%H R. H. Hardin, <a href="/A305637/b305637.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +3*a(n-2) +9*a(n-3) -11*a(n-4) -37*a(n-5) -56*a(n-6) +14*a(n-7) +135*a(n-8) +177*a(n-9) +40*a(n-10) -179*a(n-11) -188*a(n-12) -61*a(n-13) +34*a(n-14) +3*a(n-15) for n>17.
%e Some solutions for n=5
%e ..0..0..1. .0..1..1. .0..0..0. .0..1..0. .0..0..0. .0..1..1. .0..0..0
%e ..1..1..1. .0..1..1. .1..0..0. .0..0..0. .0..0..1. .0..0..0. .0..0..0
%e ..1..1..1. .1..1..1. .1..0..0. .0..0..0. .1..0..0. .0..0..0. .0..0..0
%e ..0..1..0. .1..1..1. .1..1..0. .0..0..0. .1..0..1. .1..0..0. .0..0..0
%e ..0..1..0. .1..1..1. .1..1..0. .0..1..0. .1..1..0. .1..0..0. .0..0..0
%Y Cf. A305642.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 07 2018
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