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%I #7 Jan 14 2019 09:04:39
%S 3,12,32,100,248,620,1456,3380,7656,17148,37920,83140,180824,390796,
%T 839824,1796180,3825352,8116764,17165568,36195300,76118840,159694252,
%U 334301552,698429300,1456510888,3032326460,6303262176,13083742980
%N Number of n X 2 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="/A268768/b268768.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4) for n>5.
%F Conjectures from _Colin Barker_, Jan 14 2019: (Start)
%F G.f.: x*(3 + 6*x - x^2 + 12*x^3 + 12*x^4) / ((1 + x)^2*(1 - 2*x)^2).
%F a(n) = (4/27)*(7*((-1)^n-2^n) + 3*((-1)^n + 2^(2+n))*n) for n>1.
%F (End)
%e Some solutions for n=4:
%e ..1..2. .0..1. .2..1. .0..1. .1..0. .2..1. .0..1. .1..1. .0..0. .2..1
%e ..2..2. .0..0. .2..2. .1..0. .0..1. .2..2. .0..0. .2..2. .0..0. .1..2
%e ..1..1. .1..0. .2..1. .0..0. .0..0. .1..2. .0..0. .2..2. .0..1. .2..2
%e ..0..0. .0..1. .1..2. .1..0. .0..1. .1..2. .1..1. .1..2. .1..0. .2..1
%Y Column 2 of A268774.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 13 2016
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