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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 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

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