A103937 Number of unrooted n-edge maps in the plane (planar map with a distinguished outside face).

1, 2, 6, 26, 150, 1032, 8074, 67086, 586752, 5317226, 49592424, 473357994, 4606116310, 45554761836, 456848968518, 4637014782748, 47563495004742, 492422043299964, 5140194991046122, 54053208147441474, 572191817441284272, 6093471300213162072, 65245904156725935906

Offset: 0

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

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• V. A. Liskovets and T. R. Walsh, Counting unrooted maps on the plane, Advances in Applied Math., 36, No.4 (2006), 364-387.

Crossrefs

Antidiagonal sums of A380240.

Cf. A005159, A006384.

Programs

Mathematica

a[n_] := (1/(2n)) (3^n Binomial[2n, n]/(n+1) + Sum[Boole[0Jean-François Alcover, Aug 28 2019 *)

PARI

a(n) = {if(n==0, 1, (3^n*binomial(2*n,n)/(n+1) + sumdiv(n, k, if(kAndrew Howroyd, Jan 22 2025

Formula

a(n)=(1/(2n))[3^n*binomial(2n, n)/(n+1) +sum_{0A000010, q(n)=0 if n is even and q(n)=3^((n-1)/2)binomial(n-1, (n-1)/2)/(n+1) if n is odd.

Extensions

a(0)=1 prepended by Andrew Howroyd, Jan 21 2025