A006409 Number of nonseparable rooted toroidal maps with n + 4 edges and n + 1 vertices. (Formerly M4742)

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

2,1

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.

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

Prog

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

Crossrefs

Column 3 of A342989.

Sequence in context: A223146 A365175 A239765 * A173813 A249643 A056174

Adjacent sequences: A006406 A006407 A006408 * A006410 A006411 A006412

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved