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A045310 Number of matchings in n-cube. 3
2, 7, 108, 41025, 13803794944, 7174574164703330195841 (list; graph; refs; listen; history; text; internal format)



I.e., Hosoya index of the n-hypercube graph Q_n. - Eric W. Weisstein, Jul 11 2011

a(4) = A033532(1), a(5) = A033532(2).

a(3) = A033516(2) = A033535(2). - Alois P. Heinz, Dec 09 2013

Equivalently, the number of decompositions of an n-dimensional cube of size 2 into (zero or more) unit cubes (1x1x...x1) and "dominoes" (2x1x1x...x1). - Hugo van der Sanden, Nov 30 2016


Table of n, a(n) for n=1..6.

Per Hakan Lundow, Computation of matching polynomials and the number of 1-factors in polygraphs, Research report, No 12, 1996, Department of Math., Umea University, Sweden.

Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

Per Hakan Lundow, GrafPack (Mathematica package).

Hugo van der Sanden, find2: Proof of concept in perl

Hugo van der Sanden, find2c.c: Fast version in C.

Eric Weisstein's World of Mathematics, Hosoya Index

Eric Weisstein's World of Mathematics, Hypercube Graph


From Max Alekseyev, Nov 16 2009: (Start)

E.g. for n=2, we have

1 matching of size 0 (i.e. the empty matching)

4 matchings of size 1 (i.e. an edge)

2 matchings of size 2 (that are the perfect matchings).

So a(2) = 1 + 4 + 2 = 7, whereas A005271(2) = 2. (End)


For Perl and C programs see Links section.


For perfect matchings see A005271.

For matching polynomials, see A192437.

Cf. A033532.

Sequence in context: A162634 A235470 A072664 * A224445 A000157 A264999

Adjacent sequences:  A045307 A045308 A045309 * A045311 A045312 A045313




Per H. Lundow



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Last modified March 29 21:48 EDT 2017. Contains 284288 sequences.