%I #4 Mar 09 2018 17:20:35
%S 1,2,6,18,23,89,230,552,1555,4206,11450,31045,85225,232290,634516,
%T 1734730,4739435,12951941,35393508,96729068,264330479,722375126,
%U 1974121998,5394894605,14743271893,40290668634,110107068086,300902363502
%N Number of nX3 0..1 arrays with every element equal to 0, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Column 3 of A300605.
%H R. H. Hardin, <a href="/A300600/b300600.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) +4*a(n-2) +5*a(n-3) -3*a(n-4) -12*a(n-5) -9*a(n-6) +13*a(n-7) -6*a(n-8) -21*a(n-9) -5*a(n-10) +44*a(n-11) +23*a(n-12) +17*a(n-13) -70*a(n-14) -9*a(n-15) +82*a(n-16) -103*a(n-17) +91*a(n-18) -18*a(n-19) -82*a(n-20) +96*a(n-21) -56*a(n-22) +16*a(n-23) +21*a(n-24) -29*a(n-25) +14*a(n-26) -3*a(n-27) -2*a(n-28) +3*a(n-29) -a(n-30) for n>31
%e Some solutions for n=5
%e ..0..0..0. .0..0..1. .0..1..1. .0..0..0. .0..1..1. .0..0..1. .0..1..1
%e ..0..1..0. .0..1..1. .1..1..1. .0..1..0. .1..1..1. .0..1..1. .1..1..1
%e ..0..0..0. .1..0..1. .1..0..0. .0..0..1. .1..0..1. .0..0..0. .1..0..1
%e ..1..1..0. .1..1..0. .1..0..1. .1..1..1. .1..1..0. .0..1..0. .0..0..1
%e ..1..0..0. .1..0..0. .1..1..1. .1..1..0. .1..0..0. .0..0..0. .0..1..1
%Y Cf. A300605.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 09 2018