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A360786
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Number of ways to place two dimers on an n-cube.
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1
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0, 2, 42, 400, 2840, 17376, 97440, 516608, 2634624, 13058560, 63320576, 301707264, 1417009152, 6575120384, 30195425280, 137430827008, 620604391424, 2783097520128, 12403773407232, 54975376916480, 242441862512640, 1064326263734272, 4653131038195712, 20266193591992320
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OFFSET
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1,2
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COMMENTS
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Equivalently, a(n) is the number of 2-matchings in the n-hypercube graph. A 2-matching is a pair of edges that do not share a vertex.
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LINKS
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FORMULA
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a(n) = A192437(n, 2^(n-1)-2) for n > 1.
a(n) = 2^(n-2)*n*(1 - 2*n + n*2^(n-1)).
a(n) = 18*a(n-1) - 132*a(n-2) + 504*a(n-3) - 1056*a(n-4) + 1152*a(n-5) - 512*a(n-6) for n > 6.
G.f.: 2*x^2*(1 + 3*x - 46*x^2 + 88*x^3)/((1 - 2*x)*(1 - 4*x))^3.
(End)
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EXAMPLE
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The a(2) = 2 2-matchings are:
o---o o o
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o---o o o
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PROG
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(PARI) a(n) = 2^(n-2)*n*(1 - 2*n + n*2^(n-1)) \\ Andrew Howroyd, Feb 20 2023
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CROSSREFS
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Third from last terms in rows of A192437.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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