login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Index entries for sequences related to dominoes

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 18 21:04 EST 2018. Contains 317331 sequences. (Running on oeis4.)