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).

1, 2, 9, 38, 214, 1253, 7925, 51620, 346307, 2365886, 16421359, 115384738, 819276830, 5868540399, 42357643916, 307753571520, 2249048959624, 16520782751969, 121915128678131, 903391034923548, 6719098772562182

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-François Alcover, Sep 18 2016 *)

Crossrefs

Cf. A069720, A069727, A005470.

Sequence in context: A370397 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