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A112944 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. 4
1, 2, 7, 39, 308, 3013, 33300, 394340, 4878109, 62232321, 812825244, 10818489817, 146250545528, 2003199281223, 27747288947266, 388087900316025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

M. Bousquet, G. Labelle and P. Leroux, Enumeration of planar two-face maps, Discrete Math., vol. 222 (2000), 1-25.

LINKS

Table of n, a(n) for n=0..15.

Z. C. Gao, V. A. Liskovets and N. C. Wormald, Enumeration of unrooted odd-valent regular planar maps, Preprint, 2005.

FORMULA

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.

EXAMPLE

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.

CROSSREFS

Cf. A005470, A112945, A113181, A113182.

Sequence in context: A054133 A032118 A125660 * A060073 A187806 A103365

Adjacent sequences:  A112941 A112942 A112943 * A112945 A112946 A112947

KEYWORD

nonn

AUTHOR

Valery A. Liskovets, Oct 10 2005

STATUS

approved

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Last modified November 27 15:39 EST 2014. Contains 250224 sequences.