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Search: id:A112944
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| A112944 |
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Number of unrooted regular odd-valent planar maps with 2 vertices; maps are considered up to orientation-preserving homeomorphisms and the vertices are of valency 2n+1. |
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5
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| 1, 2, 7, 39, 308, 3013, 33300, 394340, 4878109, 62232321, 812825244, 10818489817, 146250545528, 2003199281223, 27747288947266, 388087900316025
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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M. Bousquet, G. Labelle and P. Leroux, Enumeration of planar two-face maps, Discrete Math., vol. 222 (2000), 1-25.
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LINKS
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Z. C. Gao, V. A. Liskovets and N. C. Wormald, Enumeration of unrooted odd-valent regular planar maps, Preprint, 2005.
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FORMULA
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a(n)=(1/2)binomial(2n, n)+(1/(4n+2))sum_{k|(2n+1)}phi(k)* binomial(2*floor(n/k), floor(n/k))^2, where phi(k) is the Euler function A000010.
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EXAMPLE
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There exist 2 planar maps with two 3-valent vertices: a map with three parallel edges and a map with one loop in each vertex and a link. Therefore a(1)=2.
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CROSSREFS
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Cf. A005470, A112945, A113181, A113182.
Sequence in context: A054133 A032118 A125660 this_sequence A060073 A103365 A145086
Adjacent sequences: A112941 A112942 A112943 this_sequence A112945 A112946 A112947
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KEYWORD
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nonn
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AUTHOR
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Valery A. Liskovets (liskov(AT)im.bas-net.by), Oct 10 2005
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