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Number of nX2 n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.
Column 2 of A268789.
Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-3) - 6*a(n-4) - 4*a(n-5) - a(n-6).
Empirical g.f.: x*(1 + 3*x + 4*x^2 + x^3) / (1 - x - 2*x^2 - x^3)^2. - Colin Barker, Jan 15 2019
Some solutions for n=4:
Cf. Column 2 of A268789.
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R. H. Hardin, <a href="/A268783/b268783.txt">Table of n, a(n) for n = 1..210</a>
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Number of nX2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.
1, 5, 17, 48, 131, 338, 850, 2091, 5061, 12095, 28608, 67095, 156244, 361652, 832757, 1908885, 4358285, 9915728, 22489147, 50862918, 114743814, 258261695, 580072917, 1300393467, 2910078592, 6501783407, 14504787560, 32313853992, 71896385513
1,2
Column 2 of A268789.
Empirical: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6)
Some solutions for n=4
..1..0. .1..1. .0..0. .0..0. .0..0. .1..1. .0..0. .1..0. .0..0. .0..0
..0..0. .0..0. .1..0. .1..1. .0..0. .0..0. .1..1. .1..0. .1..0. .0..1
..0..1. .0..0. .1..0. .0..0. .1..1. .1..0. .0..0. .0..0. .0..1. .0..1
..1..0. .0..1. .0..1. .1..0. .0..0. .0..1. .0..0. .0..1. .1..0. .0..0
Cf. A268789.
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R. H. Hardin, Feb 13 2016
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