A006409 Number of nonseparable rooted toroidal maps with n + 4 edges and n + 1 vertices.

10, 190, 1568, 8344, 33580, 111100, 317680, 811096, 1891318, 4094090, 8328320, 16071120, 29636984, 52540472, 89974880, 149432720, 241497410, 380839382, 587453856, 888181800, 1318560100, 1925051700, 2767711440, 3923348520, 5489251950, 7587551010, 10370288640

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The number of faces is 3. - Andrew Howroyd, Apr 05 2021

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..1000
• T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.

Crossrefs

Column 3 of A342989.

Programs

PARI

a(n) = {binomial(n + 4, 6)*(29*n^3 + 108*n^2 - 11*n - 12)/63} \\ Andrew Howroyd, Apr 05 2021

Formula

a(n) = 10 * binomial(n + 4, 6) + 120 * binomial(n + 4, 7) + 328 * binomial(n + 4, 8) + 232 * binomial(n + 4, 9) [From Walsh]. - Sean A. Irvine, Apr 03 2017

a(n) = binomial(n + 4, 6)*(29*n^3 + 108*n^2 - 11*n - 12)/63. - Andrew Howroyd, Apr 05 2021

Extensions

Terms a(10) and beyond from Andrew Howroyd, Apr 05 2021