A360786 Number of ways to place two dimers on an n-cube.
0, 2, 42, 400, 2840, 17376, 97440, 516608, 2634624, 13058560, 63320576, 301707264, 1417009152, 6575120384, 30195425280, 137430827008, 620604391424, 2783097520128, 12403773407232, 54975376916480, 242441862512640, 1064326263734272, 4653131038195712, 20266193591992320
Offset: 1
Examples
The a(2) = 2 2-matchings are:
o---o o o
| |
o---o o o
Links
- Krishnan Balasubramanian, Topological Indices, Graph Spectra, Entropies, Laplacians, and Matching Polynomials of n-Dimensional Hypercubes, Symmetry. 2023; 15(2):557.
- Eric Weisstein's World of Mathematics, Hypercube Graph.
- Eric Weisstein's World of Mathematics, Matching-Generating Polynomial.
- Index entries for linear recurrences with constant coefficients, signature (18,-132,504,-1056,1152,-512).
Crossrefs
Programs
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PARI
a(n) = 2^(n-2)*n*(1 - 2*n + n*2^(n-1)) \\ Andrew Howroyd, Feb 20 2023
Formula
a(n) = A192437(n, 2^(n-1)-2) for n > 1.
From Andrew Howroyd, Feb 20 2023: (Start)
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)
Extensions
Terms a(13) and beyond from Andrew Howroyd, Feb 20 2023
Comments