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%I #8 Jan 29 2019 15:06:46
%S 7,840,45360,2005080,80724000,3078006120,113260615440,4064194275960,
%T 143136593671680,4968778108446600,170509976205204720,
%U 5796622762505510040,195530524142139886560,6552338022044877818280,218340123666185993749200
%N Number of n X 2 0..6 arrays with some element plus some horizontally or vertically adjacent neighbor totalling six exactly once.
%H R. H. Hardin, <a href="/A269896/b269896.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 62*a(n-1) - 961*a(n-2) for n>3.
%F Conjectures from _Colin Barker_, Jan 29 2019: (Start)
%F G.f.: 7*x*(1 + 58*x + x^2) / (1 - 31*x)^2.
%F a(n) = 840 * 31^(n-3) * (23*n-15) for n>1.
%F (End)
%e Some solutions for n=3:
%e ..2..1. .1..5. .2..2. .2..4. .4..2. .3..5. .4..2. .3..6. .0..0. .4..3
%e ..5..6. .4..6. .4..6. .6..1. .6..6. .3..4. .3..5. .4..2. .2..5. .5..1
%e ..1..1. .1..6. .1..1. .6..3. .3..2. .6..3. .4..5. .1..6. .0..1. .4..3
%Y Column 2 of A269902.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 07 2016
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