%I #8 Jan 15 2019 07:54:09
%S 12,32,112,446,1524,5214,17000,54822,173244,541910,1676448,5146030,
%T 15683076,47518926,143238872,429867830,1285009740,3828046534,
%U 11368576272,33669165246,99465517716,293175780030,862355454792,2531766659654
%N Number of n X 3 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
%H R. H. Hardin, <a href="/A268769/b268769.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n1) + 2*a(n2)  16*a(n3)  a(n4) + 12*a(n5)  4*a(n6) for n>8.
%F Empirical g.f.: 2*x*(6  8*x  20*x^2 + 63*x^3 + 20*x^4  47*x^5 + 4*x^6 + 4*x^7) / (1  2*x  3*x^2 + 2*x^3)^2.  _Colin Barker_, Jan 15 2019
%e Some solutions for n=4:
%e ..1..0..0. .1..0..0. .0..0..0. .1..2..1. .1..1..0. .2..2..2. .1..2..1
%e ..0..0..0. .1..0..0. .1..1..0. .1..2..2. .0..0..0. .1..2..2. .1..2..2
%e ..1..0..1. .0..0..0. .0..0..0. .2..2..1. .0..0..0. .2..2..1. .2..2..2
%e ..0..0..1. .1..0..0. .1..0..0. .1..2..2. .1..0..1. .2..1..2. .1..2..2
%Y Column 3 of A268774.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 13 2016
