A118449 Number of rooted n-edge one-vertex maps on a non-orientable genus-4 surface (dually: one-face maps).

0, 488, 11660, 160680, 1678880, 14771680, 115457832, 827303280, 5545466520, 35257287120, 214730922120, 1262004908528, 7197437563680, 40007524376960, 217501266966160, 1159737346931040, 6079078540464072, 31385516059734960

Offset

3,2

Comments

One-vertex maps on a non-orientable genus-3 surface are counted by A118448. Such maps are also called bouquets of loops (and their duals are called unicellular maps).

References

E. R. Canfield, Calculating the number of rooted maps on a surface, Congr. Numerantium, 76 (1990), 21-34.

D. M. Jackson and T. I. Visentin, An atlas of the smaller maps in orientable and nonorientable surfaces. CRC Press, Boca Raton, 2001.

Links

Table of n, a(n) for n=3..20.

Didier Arquès and Alain Giorgetti, Counting rooted maps on a surface, Theoret. Comput. Sci. 234 (2000), no. 1-2, 255--272. MR1745078 (2001f:05078).

Formula

O.g.f.: -(R-1)^4(R+1)^3(65R^3+337R^2-433R-945)/(256R^11), where R=sqrt(1-4x).

a(n) ~ n^(9/2) * 2^(2*n-3) / sqrt(Pi) * (1 - 2*sqrt(Pi)/(3*sqrt(n))). - Vaclav Kotesovec, Oct 27 2024

Mathematica

With[{r=Sqrt[1-4x]}, Drop[CoefficientList[Series[-(r-1)^4 (r+1)^3 (65r^3+ 337r^2- 433r-945)/(256r^11), {x, 0, 20}], x], 3]] (* Harvey P. Dale, Aug 05 2019 *)

Crossrefs

Cf. A118448. A diagonal of A214806.

Sequence in context: A045011 A253336 A205315 * A223398 A214334 A201835

Adjacent sequences: A118446 A118447 A118448 * A118450 A118451 A118452

Keyword

nonn

Author

Valery A. Liskovets, May 04 2006

Status

approved