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

Author

Valery A. Liskovets, May 04 2006

Keywords

• nonn

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

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

Crossrefs

Cf. A118448. A diagonal of A214806.

Programs

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 *)

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