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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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, 5474206895126243, 77795972452841542, 1112947041203866164, 16016508647052018408, 231727628211887783830, 3368855109532696440867 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

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

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.

PROG

(PARI) a(n) = binomial(2*n, n)/2 + sumdiv(2*n+1, k, eulerphi(k)* binomial(2*(n\k), (n\k))^2)/(4*n+2); \\ Michel Marcus, Oct 14 2015

CROSSREFS

Cf. A005470, A112945, A113181, A113182.

Sequence in context: A266310 A032118 A125660 * A060073 A187806 A103365

Adjacent sequences:  A112941 A112942 A112943 * A112945 A112946 A112947

KEYWORD

nonn

AUTHOR

Valery A. Liskovets, Oct 10 2005

EXTENSIONS

More terms from Michel Marcus, Oct 14 2015

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 December 11 00:29 EST 2016. Contains 279033 sequences.