

A112944


Number of unrooted regular oddvalent planar maps with 2 vertices; maps are considered up to orientationpreserving 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
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OFFSET

0,2


REFERENCES

M. Bousquet, G. Labelle and P. Leroux, Enumeration of planar twoface maps, Discrete Math., vol. 222 (2000), 125.


LINKS

Table of n, a(n) for n=0..15.
Z. C. Gao, V. A. Liskovets and N. C. Wormald, Enumeration of unrooted oddvalent 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 3valent 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



