A006415 Number of nonseparable toroidal tree-rooted maps with n + 3 edges and n + 1 vertices. (Formerly M3705)

4, 104, 1020, 6092, 26670, 94128, 283338, 754380, 1821534, 4061200

Offset

0,1

Comments

The number of faces is 2. - 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

Table of n, a(n) for n=0..9.

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

Conjecture: a(n) = 4 * binomial(n + 4, n) + 84 * binomial(n + 4, n - 1) + 456 * binomial(n + 4, n - 2) + 996 * binomial(n + 4, n - 3) + 950 * binomial(n + 4, n - 4) + 330 * binomial(n + 5, n - 5). - Sean A. Irvine, Apr 03 2017

Crossrefs

Cf. A006414, A006441.

Sequence in context: A331456 A211150 A281534 * A333434 A181396 A354063

Adjacent sequences: A006412 A006413 A006414 * A006416 A006417 A006418

Keyword

nonn,more

Author

N. J. A. Sloane

Status

approved