

A045310


Number of matchings in ncube.


4




OFFSET

0,2


COMMENTS

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 ndimensional cube of size 2 into (zero or more) unit cubes (1 X 1 X ... X 1) and "dominoes" (2 X 1 X 1 X ... X 1).  Hugo van der Sanden, Nov 30 2016


LINKS

Table of n, a(n) for n=0..6.
Per Hakan Lundow, Computation of matching polynomials and the number of 1factors 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, Hypercube Graph
Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching


EXAMPLE

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)


PROG

For Perl and C programs see Links section.


CROSSREFS

For perfect matchings see A005271.
For matching polynomials, see A192437, A302235.
Cf. A033532.
Sequence in context: A162634 A235470 A072664 * A224445 A000157 A264999
Adjacent sequences: A045307 A045308 A045309 * A045311 A045312 A045313


KEYWORD

nonn,hard,more


AUTHOR

Per H. Lundow


STATUS

approved



