A006469 Number of rooted toroidal maps with 2 faces, n vertices and no isthmuses. (Formerly M4727)

10, 79, 340, 1071, 2772, 6258, 12768, 24090, 42702, 71929, 116116, 180817, 273000, 401268, 576096, 810084, 1118226, 1518195, 2030644, 2679523, 3492412, 4500870, 5740800, 7252830, 9082710, 11281725, 13907124, 17022565, 20698576, 25013032, 30051648, 35908488

Offset

1,1

Comments

A map on a torus has genus 1.

References

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

Links

Colin Barker, 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

G.f.: x/(x-1)^7*(3*x^2-9*x-10). - Simon Plouffe, Master's thesis, Uqam 1992

From Colin Barker, Apr 22 2017: (Start)

a(n) = (n*(474 + 1247*n + 1215*n^2 + 545*n^3 + 111*n^4 + 8*n^5)) / 360.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Prog

(PARI) Vec(x*(10 + 9*x - 3*x^2) / (1 - x)^7 + O(x^40)) \\ Colin Barker, Apr 22 2017

Crossrefs

Column 2 of A343092.

Sequence in context: A222701 A283658 A160655 * A288630 A081905 A016138

Adjacent sequences: A006466 A006467 A006468 * A006470 A006471 A006472

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Name improved by Sean A. Irvine, Apr 21 2017

Status

approved