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%I #8 Mar 21 2018 09:54:20
%S 3,24,120,504,1944,7128,25272,87480,297432,997272,3306744,10865016,
%T 35429400,114791256,369882936,1186176312,3788111448,12053081880,
%U 38225488248,120875192568,381221761176,1199453833944,3765727153080
%N Number of n X 2 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.
%C Column 2 of A268639.
%H R. H. Hardin, <a href="/A268633/b268633.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 9*a(n-2) for n>3.
%F Conjectures from _Colin Barker_, Mar 21 2018: (Start)
%F G.f.: 3*x*(1 + x)^2 / (1 - 3*x)^2.
%F a(n) = 8*3^(n-2)*(2*n-1) for n>1.
%F (End)
%e Some solutions for n=8:
%e ..0..1. .1..2. .2..1. .1..2. .2..2. .0..0. .0..0. .2..2. .1..2. .1..2
%e ..1..0. .2..1. .1..0. .2..2. .1..2. .0..0. .0..0. .2..1. .2..1. .2..1
%e ..2..1. .1..0. .2..1. .2..1. .2..1. .0..1. .0..0. .2..1. .2..2. .2..1
%e ..2..1. .0..0. .1..0. .0..0. .2..2. .1..2. .1..0. .1..2. .1..2. .2..2
%e ..2..2. .0..0. .2..2. .1..0. .2..2. .0..1. .0..1. .2..2. .0..0. .1..2
%e ..2..1. .0..0. .2..2. .0..1. .0..1. .0..0. .1..0. .2..2. .1..0. .2..1
%e ..1..0. .1..2. .2..2. .0..0. .0..0. .2..1. .2..2. .2..1. .0..0. .2..2
%e ..0..0. .0..1. .2..2. .0..0. .0..0. .2..2. .2..2. .1..2. .0..1. .2..2
%Y Cf. A268639.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 09 2016