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 A006421 Number of rooted planar maps with 4 vertices and n faces and no isthmuses. (Formerly M5211) 2
 1, 30, 449, 4795, 41850, 319320, 2213665, 14283280, 87169790, 508887860, 2865204762, 15654301865, 83388235348, 434685964540, 2223970137825, 11194499812388, 55546566721430, 272142754971892, 1318317357277470, 6321681903231990, 30037740651227756, 141545610360126400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 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..500 T. R. S. Walsh, A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259. FORMULA G.f.: x^2*(1 + 9*g - 9*g^2 - 20*g^3 + 20*g^4)/((1 - g)^5*(1 - 2*g)^8)) where g/x is the g.f. of A000108. - Andrew Howroyd, Apr 02 2021 PROG (PARI) seq(n)={my(g=x*(1-sqrt(1-4*x + O(x^n)))/(2*x)); Vec((1 + 9*g - 9*g^2 - 20*g^3 + 20*g^4)/((1 - g)^5*(1 - 2*g)^8))} \\ Andrew Howroyd, Apr 02 2021 CROSSREFS A diagonal of A342981. Sequence in context: A280856 A281602 A307917 * A035710 A341559 A042746 Adjacent sequences:  A006418 A006419 A006420 * A006422 A006423 A006424 KEYWORD nonn AUTHOR EXTENSIONS a(13) and title improved by Sean A. Irvine, Apr 06 2017 Terms a(14) and beyond from Andrew Howroyd, Apr 02 2021 STATUS approved

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Last modified November 27 09:19 EST 2021. Contains 349365 sequences. (Running on oeis4.)