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 A045310 Number of matchings in n-cube. 4
 1, 2, 7, 108, 41025, 13803794944, 7174574164703330195841 (list; graph; refs; listen; history; text; internal format)
 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 n-dimensional 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 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, 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 STATUS approved

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Last modified December 9 08:20 EST 2019. Contains 329877 sequences. (Running on oeis4.)