A006422 Number of rooted toroidal maps with 2 faces and n vertices and without separating cycles or isthmuses.

4, 47, 240, 831, 2282, 5362, 11256, 21690, 39072, 66649, 108680, 170625, 259350, 383348, 552976, 780708, 1081404, 1472595, 1974784, 2611763, 3410946, 4403718, 5625800, 7117630, 8924760, 11098269, 13695192, 16778965, 20419886, 24695592, 29691552, 35501576

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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 = 1..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.
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Column 2 of A343090.

Programs

Mathematica

LinearRecurrence[{7,-21,35,-35,21,-7,1},{4,47,240,831,2282,5362,11256},40] (* Harvey P. Dale, May 15 2023 *)

PARI

a(n) = {n*(n + 1)*(n + 2)*(8*n^3 + 87*n^2 + 148*n - 3)/360}

Formula

From Colin Barker, Apr 09 2013: (Start)

a(n) = n*(n + 1)*(n + 2)*(8*n^3 + 87*n^2 + 148*n - 3)/360.

G.f.: x*(2*x^3+5*x^2-19*x-4) / (x-1)^7. (End)

Extensions

Name clarified and terms a(11) and beyond from Andrew Howroyd, Apr 04 2021