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

1,1

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

Table of n, a(n) for n=1..20.

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

Formula

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

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 *)

Crossrefs

Cf. A069720, A103944.

Sequence in context: A074618 A108436 A088754 * A378460 A111713 A377103

Adjacent sequences: A103942 A103943 A103944 * A103946 A103947 A103948

Keyword

easy,nonn

Author

Valery A. Liskovets, Mar 17 2005

Status

approved