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

Author

Valery A. Liskovets, Apr 07 2002

Keywords

• easy
• nice
• nonn

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.

Crossrefs

Cf. A069720, A069727, A005470.

Programs

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 *)

Formula

There is an easy formula.

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