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 A028420 Number of monomer-dimer tilings of n X n chessboard. 8
 1, 7, 131, 10012, 2810694, 2989126727, 11945257052321, 179788343101980135, 10185111919160666118608, 2172138783673094193937750015, 1743829823240164494694386437970640, 5270137993816086266962874395450234534887 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also the total number of matchings (not necessarily perfect ones; i.e., Hosoya index) in the n X n grid. - Andre Poenitz (poenitz(AT)htwm.de), Nov 20 2003 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 406-412. LINKS Jennifer Henry, Table of n, a(n) for n = 1..21 [From S. R. Finch, Jan 30 2009] Ahrens, J. H. Paving the chessboard. J. Combin. Theory Ser. A 31(1981), no. 3, 277--288. MR0635371 (84d:05009). See Table I. - N. J. A. Sloane, Mar 27 2012 S. R. Finch, Two Dimensional Monomer-Dimer Constant P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 362 Eric Weisstein's World of Mathematics, Grid Graph Eric Weisstein's World of Mathematics, Hosoya Index Eric Weisstein's World of Mathematics, Independent Edge Set Eric Weisstein's World of Mathematics, Matching D. Zeilberger, Source MATHEMATICA Table[With[{g = GridGraph[{n, n}]}, Count[Subsets[EdgeList[g], Length @ Flatten @ FindIndependentEdgeSet[g]], _?(IndependentEdgeSetQ[g, #] &)]], {n, 4}] (* Eric W. Weisstein, May 28 2017 *) CROSSREFS Cf. A004003. A diagonal of A210662. Row sums of A242861. Sequence in context: A201308 A170912 A099601 * A220257 A220321 A247597 Adjacent sequences:  A028417 A028418 A028419 * A028421 A028422 A028423 KEYWORD nonn,nice AUTHOR Jennifer Henry, Shalosh B. Ekhad, and Steven Finch EXTENSIONS Broken links corrected by Steven Finch, Jan 27 2009 STATUS approved

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Last modified January 23 08:51 EST 2019. Contains 319376 sequences. (Running on oeis4.)