%I #4 Mar 07 2018 07:30:28
%S 3,2,4,7,6,17,34,57,80,164,302,526,885,1647,2996,5296,9259,16753,
%T 30075,53468,94738,169873,303898,541631,964444,1724067,3079837,
%U 5493915,9797538,17495715,31235953,55738172,99453077,177534256,316897514,565552854
%N Number of nX3 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Column 3 of A300506.
%H R. H. Hardin, <a href="/A300501/b300501.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-2) +2*a(n-3) -7*a(n-4) -8*a(n-5) -5*a(n-6) +10*a(n-7) +34*a(n-8) +10*a(n-9) -54*a(n-10) -52*a(n-11) +26*a(n-12) +72*a(n-13) +26*a(n-14) -40*a(n-15) -49*a(n-16) -16*a(n-17) +21*a(n-18) +36*a(n-19) +14*a(n-20) -12*a(n-21) -10*a(n-22) -4*a(n-23) -a(n-24) +2*a(n-25) +a(n-26) for n>31
%e All solutions for n=5
%e ..0..1..0. .0..0..0. .0..1..0. .0..1..0. .0..0..1. .0..0..0
%e ..0..0..1. .1..0..0. .0..0..1. .0..0..1. .1..1..0. .1..0..0
%e ..0..0..0. .1..0..1. .0..1..0. .0..0..1. .0..1..1. .0..1..0
%e ..1..0..0. .0..0..1. .0..0..1. .1..0..0. .0..1..1. .1..0..0
%e ..0..1..0. .0..0..0. .0..0..0. .0..1..1. .1..0..1. .0..1..0
%Y Cf. A300506.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 07 2018