A006422 Number of rooted toroidal maps with 2 faces and n vertices and without separating cycles or isthmuses. (Formerly M3684)

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

1,1

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).

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)

Mathematica

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

Prog

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

Crossrefs

Column 2 of A343090.

Sequence in context: A107766 A065777 A193485 * A301278 A186677 A277654

Adjacent sequences: A006419 A006420 A006421 * A006423 A006424 A006425

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved