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%I #8 Jan 18 2019 09:58:15
%S 12,48,348,2136,12228,67104,357756,1867560,9593844,48665904,244357740,
%T 1216672824,6015296484,29561944128,144531868764,703461546312,
%U 3410368965588,16475694411600,79347347565132,381071870841432
%N Number of n X 3 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
%H R. H. Hardin, <a href="/A269030/b269030.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4) for n>5.
%F Empirical g.f.: 12*x*(1 - 6*x + 18*x^2 - 16*x^3 + 4*x^4) / (1 - 5*x + 2*x^2)^2. - _Colin Barker_, Jan 18 2019
%e Some solutions for n=4:
%e ..1..2..2. .2..2..2. .1..0..2. .0..0..0. .2..2..1. .0..1..0. .2..1..0
%e ..2..2..2. .2..1..2. .1..2..1. .0..0..0. .1..2..2. .1..0..0. .0..1..2
%e ..2..1..0. .2..2..2. .2..2..1. .0..1..0. .2..2..1. .0..0..0. .0..1..0
%e ..2..1..0. .2..1..0. .2..2..1. .2..0..0. .2..1..2. .0..0..0. .0..0..2
%Y Column 3 of A269035.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 18 2016