%I #4 Jan 07 2018 10:58:36
%S 0,2,4,13,62,222,820,3159,11882,44870,169628,640493,2419796,9141186,
%T 34529922,130440579,492746204,1861372064,7031443952,26561657355,
%U 100338117488,379032792052,1431817164232,5408768126291,20431919210138
%N Number of nX3 0..1 arrays with every element equal to 2, 3 or 4 king-move adjacent elements, with upper left element zero.
%C Column 3 of A297866.
%H R. H. Hardin, <a href="/A297861/b297861.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +4*a(n-2) -13*a(n-4) -8*a(n-5) -3*a(n-6) -4*a(n-7) +44*a(n-8) +33*a(n-9) -55*a(n-10) -42*a(n-11) +26*a(n-12) +16*a(n-13) -4*a(n-14) for n>16
%e Some solutions for n=7
%e ..0..0..0. .0..0..1. .0..1..1. .0..0..1. .0..0..0. .0..0..1. .0..0..0
%e ..0..1..0. .0..1..1. .0..0..1. .0..1..1. .0..1..0. .0..1..1. .0..1..0
%e ..1..1..0. .0..1..1. .1..1..0. .1..0..0. .1..1..0. .1..0..0. .1..1..0
%e ..1..0..0. .1..0..0. .1..0..0. .1..1..0. .1..0..0. .1..1..0. .0..0..1
%e ..0..1..1. .0..1..0. .1..0..0. .0..1..1. .1..0..0. .1..0..0. .0..1..1
%e ..0..0..1. .1..0..1. .1..0..1. .0..0..1. .0..1..1. .1..1..0. .0..1..1
%e ..0..1..1. .1..1..1. .1..1..1. .0..1..1. .0..0..1. .1..0..0. .0..0..1
%Y Cf. A297866.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 07 2018