A103945 Number of rooted dual-unicursal n-edge maps in the plane (planar with a distinguished outside face).

2, 14, 107, 844, 6757, 54522, 441863, 3589880, 29206025, 237780982, 1936486411, 15771410420, 128431734797, 1045618229234, 8510270668815, 69241255165936, 563154350637073, 4578526894227438, 37209886138826771, 302291556342169580

Offset: 1

Author

Valery A. Liskovets, Mar 17 2005

Keywords

• easy
• nonn

References

• V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.

Links

• V. A. Liskovets and T. R. Walsh, Counting unrooted maps on the plane, Advances in Applied Math., 36, No.4 (2006), 364-387.

Crossrefs

Cf. A069720, A103944.

Programs

Mathematica

A069720[n_] := 2^(n-1) Binomial[2n-1, n];
A103944[n_] := If[n == 1, 1, n Binomial[2n, n] Sum[Binomial[n-2, k] (1/(n + 1 + k) + n/(n + 2 + k)), {k, 0, n-2}]];
a[n_] := (n+2) A069720[n] - A103944[n];
Array[a, 20] (* Jean-François Alcover, Aug 28 2019 *)

Formula

a(n)=(n+2)*A069720(n)-A103944(n).