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 A006410 Number of nonseparable rooted toroidal maps with n + 5 edges and n + 1 vertices. (Formerly M5102) 2
 20, 651, 8344, 64667, 361884, 1607125, 5997992, 19535997, 57014776, 151986562, 375470160, 869285378, 1902886024, 3966657702, 7920130544, 15220758070, 28268206764, 50910912965, 89176474920, 152305796565, 254193384900, 415363487955, 665644575960, 1047743815755 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The number of faces is 4. - Andrew Howroyd, Apr 05 2021 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 = 2..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. FORMULA a(n) = 20 * binomial(n + 6, 8) + 471 * binomial(n + 6, 9) + 2734 * binomial(n + 6, 10) + 5388 * binomial(n + 6, 11) + 3264 * binomial(n + 6, 12) [From Walsh]. - Sean A. Irvine, Apr 03 2017 a(n) = binomial(n + 6, 8)*(136*n^4 + 790*n^3 + 447*n^2 - 180*n - 24)/495. - Andrew Howroyd, Apr 05 2021 PROG (PARI) a(n) = {binomial(n + 6, 8)*(136*n^4 + 790*n^3 + 447*n^2 - 180*n - 24)/495} \\ Andrew Howroyd, Apr 05 2021 CROSSREFS Column 4 of A342989. Sequence in context: A336412 A226731 A201724 * A159874 A203136 A034404 Adjacent sequences: A006407 A006408 A006409 * A006411 A006412 A006413 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS Terms a(9) and beyond from Andrew Howroyd, Apr 05 2021 STATUS approved

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Last modified July 21 11:45 EDT 2024. Contains 374472 sequences. (Running on oeis4.)