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A268769 Number of n X 3 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

%I A268769 #8 Jan 15 2019 07:54:09
%S A268769 12,32,112,446,1524,5214,17000,54822,173244,541910,1676448,5146030,
%T A268769 15683076,47518926,143238872,429867830,1285009740,3828046534,
%U A268769 11368576272,33669165246,99465517716,293175780030,862355454792,2531766659654
%N A268769 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 A268769 R. H. Hardin, <a href="/A268769/b268769.txt">Table of n, a(n) for n = 1..210</a>
%F A268769 Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 16*a(n-3) - a(n-4) + 12*a(n-5) - 4*a(n-6) for n>8.
%F A268769 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 A268769 Some solutions for n=4:
%e A268769 ..1..0..0. .1..0..0. .0..0..0. .1..2..1. .1..1..0. .2..2..2. .1..2..1
%e A268769 ..0..0..0. .1..0..0. .1..1..0. .1..2..2. .0..0..0. .1..2..2. .1..2..2
%e A268769 ..1..0..1. .0..0..0. .0..0..0. .2..2..1. .0..0..0. .2..2..1. .2..2..2
%e A268769 ..0..0..1. .1..0..0. .1..0..0. .1..2..2. .1..0..1. .2..1..2. .1..2..2
%Y A268769 Column 3 of A268774.
%K A268769 nonn
%O A268769 1,1
%A A268769 _R. H. Hardin_, Feb 13 2016