%I #4 Feb 19 2018 15:28:29
%S 4,13,20,44,123,343,973,2774,7993,23110,66714,192997,558501,1615967,
%T 4676936,13536345,39177448,113393194,328199369,949923737,2749424053,
%U 7957828042,23032842153,66665439494,192954061684,558479378315
%N Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Column 3 of A299806.
%H R. H. Hardin, <a href="/A299801/b299801.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) -7*a(n-2) +8*a(n-3) -26*a(n-4) +34*a(n-5) -18*a(n-6) +31*a(n-7) -29*a(n-8) -20*a(n-9) +54*a(n-10) -59*a(n-11) +67*a(n-12) -85*a(n-13) +46*a(n-14) -20*a(n-15) +24*a(n-16) for n>17
%e Some solutions for n=5
%e ..0..1..1. .0..0..1. .0..1..1. .0..1..0. .0..1..0. .0..1..0. .0..0..1
%e ..0..0..1. .0..1..1. .1..0..0. .1..0..0. .0..0..0. .0..0..1. .1..1..0
%e ..0..0..0. .1..1..1. .0..0..1. .1..0..0. .1..1..1. .0..0..1. .1..0..1
%e ..1..0..0. .0..0..1. .0..0..0. .1..0..0. .1..0..1. .0..0..1. .1..1..0
%e ..1..1..0. .0..1..1. .0..1..1. .0..1..0. .1..1..1. .1..0..1. .0..0..1
%Y Cf. A299806.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 19 2018