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A118449 Number of rooted n-edge one-vertex maps on a non-orientable genus-4 surface (dually: one-face maps). 2
0, 488, 11660, 160680, 1678880, 14771680, 115457832, 827303280, 5545466520, 35257287120, 214730922120, 1262004908528, 7197437563680, 40007524376960, 217501266966160, 1159737346931040, 6079078540464072, 31385516059734960 (list; graph; refs; listen; history; text; internal format)
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

Arques, Didier; and Giorgetti, Alain. Counting rooted maps on a surface. Theoret. Comput. Sci. 234 (2000), no. 1-2, 255--272. MR1745078 (2001f:05078). - N. J. A. Sloane, Jul 27 2012

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.

FORMULA

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

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

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Last modified February 25 12:01 EST 2020. Contains 332233 sequences. (Running on oeis4.)