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A268768
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Number of n X 2 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
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1
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3, 12, 32, 100, 248, 620, 1456, 3380, 7656, 17148, 37920, 83140, 180824, 390796, 839824, 1796180, 3825352, 8116764, 17165568, 36195300, 76118840, 159694252, 334301552, 698429300, 1456510888, 3032326460, 6303262176, 13083742980
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OFFSET
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1,1
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4) for n>5.
Conjectures from Colin Barker, Jan 14 2019: (Start)
G.f.: x*(3 + 6*x - x^2 + 12*x^3 + 12*x^4) / ((1 + x)^2*(1 - 2*x)^2).
a(n) = (4/27)*(7*((-1)^n-2^n) + 3*((-1)^n + 2^(2+n))*n) for n>1.
(End)
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EXAMPLE
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Some solutions for n=4:
..1..2. .0..1. .2..1. .0..1. .1..0. .2..1. .0..1. .1..1. .0..0. .2..1
..2..2. .0..0. .2..2. .1..0. .0..1. .2..2. .0..0. .2..2. .0..0. .1..2
..1..1. .1..0. .2..1. .0..0. .0..0. .1..2. .0..0. .2..2. .0..1. .2..2
..0..0. .0..1. .1..2. .1..0. .0..1. .1..2. .1..1. .1..2. .1..0. .2..1
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CROSSREFS
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Column 2 of A268774.
Sequence in context: A037236 A309693 A288605 * A174963 A054602 A083725
Adjacent sequences: A268765 A268766 A268767 * A268769 A268770 A268771
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Feb 13 2016
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STATUS
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approved
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