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Search: id:A095340
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| A095340 |
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Total number of nodes in all labeled graphs on n nodes. |
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+0
4
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| 1, 4, 24, 256, 5120, 196608, 14680064, 2147483648, 618475290624, 351843720888320, 396316767208603648, 885443715538058477568, 3929008913747544817795072, 34662321099990647697175478272
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of perfect matchings of an n x (n+1) Aztec rectangle with the second vertex in the topmost row removed.
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REFERENCES
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N. Elkies, G. Kuperberg, M. Larsen and J. Propp, Alternating sign matrices and domino tilings, Journal of Algebraic Combinatorics {\bf 1}, 111-132, 219-234 (1992).
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LINKS
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M. Ciucu, Enumeration of perfect matchings in graphs with reflective symmetry, J. Combin. Theory Ser. A 77 (1997), no. 1, 67-97
C. Krattenthaler, Schur function identities and the number of perfect matchings of Aztec holey rectangles
Eric Weisstein's World of Mathematics, Graph Vertex
H. Helfgott and I. M. Gessel, Enumeration of tilings of diamonds and hexagons with defects
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FORMULA
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a(n) = n * 2^(n(n-1)/2). E.g. a(7) = 7 * 2^(7*6/2) = 7 * 2097152 = 14680064 - David Terr (David_C_Terr(AT)raytheon.com), Nov 08 2004
a(n)=(32a(n-1)a(n-3)-48a(n-2)^2)/a(n-4). - Michael Somos Sep 16 2005
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PROGRAM
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(PARI) a(n)=n*2^((n^2-n)/2)
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CROSSREFS
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Cf. Equals n * A006125(n).
Cf. A103904.
Sequence in context: A126391 A006088 A141013 this_sequence A141014 A077700 A080489
Adjacent sequences: A095337 A095338 A095339 this_sequence A095341 A095342 A095343
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Jun 03, 2004
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EXTENSIONS
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Edited by Ralf Stephan, Feb 21 2005
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