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A006469 Number of rooted toroidal maps with 2 faces, n vertices and no isthmuses.
(Formerly M4727)
2
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 (list; graph; refs; listen; history; text; internal format)
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
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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Name improved by Sean A. Irvine, Apr 21 2017
STATUS
approved

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Last modified April 14 13:25 EDT 2024. Contains 371661 sequences. (Running on oeis4.)