%I #6 May 20 2021 12:37:59
%S 3,6,9,26,61,154,374,941,2357,5963,15074,38168,96641,244836,620311,
%T 1571854,3983147,10093850,25579490,64823479,164276135,416311227,
%U 1055023990,2673664936,6775663297,17171047596,43515284891,110277499816
%N Number of n X 3 0..1 arrays with every element equal to 0, 1 or 3 horizontally or vertically adjacent elements, with upper left element zero.
%C Column 3 of A301541.
%H R. H. Hardin, <a href="/A301536/b301536.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) -a(n-2) -a(n-3) +2*a(n-4) -a(n-5) +3*a(n-6) -11*a(n-7) -a(n-8) +2*a(n-9) -4*a(n-10) -2*a(n-11) -a(n-12) +11*a(n-13) +3*a(n-14) +a(n-15) +2*a(n-16) +a(n-17) -a(n-18) -3*a(n-19) -a(n-20).
%e Some solutions for n=5
%e ..0..1..0. .0..1..0. .0..1..0. .0..1..0. .0..0..0. .0..1..0. .0..1..0
%e ..1..0..1. .1..0..1. .1..0..1. .0..0..0. .1..0..1. .1..0..1. .1..0..1
%e ..0..1..0. .1..1..1. .0..1..1. .0..0..0. .1..1..0. .1..0..1. .0..1..1
%e ..1..0..0. .1..1..1. .1..0..1. .0..1..0. .1..0..0. .0..1..0. .1..0..1
%e ..0..1..0. .1..0..1. .0..1..0. .1..0..1. .0..1..0. .0..1..0. .0..0..0
%Y Cf. A301541.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 23 2018