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A006422 Number of rooted toroidal maps with 2 faces and n vertices and without separating cycles or isthmuses.
(Formerly M3684)
5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name clarified and terms a(11) and beyond from Andrew Howroyd, Apr 04 2021
STATUS
approved

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Last modified April 18 12:53 EDT 2024. Contains 371780 sequences. (Running on oeis4.)