A103938 Number of rooted non-separable n-edge maps in the plane (planar with a distinguished outside face).

3, 2, 5, 18, 77, 364, 1836, 9690, 52877, 296010, 1690845, 9817080, 57769740, 343806368, 2065802056, 12515350122, 76367432013, 468922828150, 2895381678735, 17966214519330, 111977263221285, 700704492237540, 4400559613086000, 27727270719559320, 175230257041962252

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..25.

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)*A000139(n)/2.

From Peter Bala, Feb 07 2022: (Start)

a(n) = 4*A001764(n-1) - A006013(n-1).

a(n) = (3*n+6)*(3*n-4)*(3*n-5)/(n*(2*n-1)*(2*n+2))*a(n-1).

O.g.f.: A(x) = x*T(x)*(4 - T(x)), where T(x) = 1 + x*T(x)^3 is the g.f. of A001764. (End)

Mathematica

a[n_] := (n+2)(3(n-1))!/((2n-1)! n!);
Array[a, 30] (* Jean-François Alcover, Aug 29 2019 *)

Crossrefs

Cf. A000139, A001764, A006013.

Sequence in context: A214502 A077039 A269155 * A304534 A085973 A302854

Adjacent sequences: A103935 A103936 A103937 * A103939 A103940 A103941

Keyword

nonn,easy

Author

Valery A. Liskovets, Mar 17 2005

Extensions

More terms from Jean-François Alcover, Aug 29 2019

Status

approved