%I #9 Mar 21 2018 12:17:26
%S 16,180,1740,15540,132300,1090740,8787660,69580980,543538380,
%T 4200069300,32167589580,244542858420,1847388128460,13880833735860,
%U 103809654007500,773174303047860,5737767196302540,42443199898890420,313054205965641420
%N Number of n X 2 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.
%C Column 2 of A269109.
%H R. H. Hardin, <a href="/A269103/b269103.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 14*a(n-1) - 49*a(n-2) for n>3.
%F Conjectures from _Colin Barker_, Mar 21 2018: (Start)
%F G.f.: 4*x*(4 - 11*x + x^2) / (1 - 7*x)^2.
%F a(n) = 60*7^(n-3)*(8*n+5) for n>1.
%F (End)
%e Some solutions for n=4:
%e ..2..2. .2..0. .2..2. .1..0. .3..3. .3..1. .1..3. .3..1. .1..3. .1..0
%e ..0..2. .2..0. .2..3. .3..1. .3..1. .3..3. .3..1. .3..1. .1..3. .3..1
%e ..1..0. .0..2. .2..3. .1..1. .2..2. .2..2. .3..3. .1..3. .0..1. .0..1
%e ..1..0. .1..0. .1..1. .1..1. .3..3. .3..0. .1..3. .3..1. .0..0. .2..0
%Y Cf. A269109.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 19 2016