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A069724 Number of nonisomorphic unrooted unicursal planar maps with n edges (unicursal means that exactly two vertices are of odd valency; there is an Eulerian path). 7
1, 2, 9, 38, 214, 1253, 7925, 51620, 346307, 2365886, 16421359, 115384738, 819276830, 5868540399, 42357643916, 307753571520, 2249048959624, 16520782751969, 121915128678131, 903391034923548, 6719098772562182 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

V. A. Liskovets and T. R. S. Walsh, Enumeration of Eulerian and unicursal planar maps, Discr. Math., 282 (2004), 209-221.

FORMULA

There is an easy formula.

a(n) ~ 8^(n-1) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Aug 28 2019

MATHEMATICA

a[n_] := 1/(2 n) DivisorSum[n, If[OddQ[n/#], EulerPhi[n/#] 2^(#-2) Binomial[2 #, #], 0]&] + If[OddQ[n], 2^((n-3)/2) Binomial[n-1, (n-1)/2], 2^((n-6)/2) Binomial[n, n/2]]; Array[a, 21] (* Jean-Fran├žois Alcover, Sep 18 2016 *)

CROSSREFS

Cf. A069720, A069727, A005470.

Sequence in context: A249925 A162972 A202832 * A132961 A278050 A070017

Adjacent sequences:  A069721 A069722 A069723 * A069725 A069726 A069727

KEYWORD

easy,nice,nonn

AUTHOR

Valery A. Liskovets, Apr 07 2002

STATUS

approved

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)