A006421 Number of rooted planar maps with 4 vertices and n faces and no isthmuses. (Formerly M5211)

1, 30, 449, 4795, 41850, 319320, 2213665, 14283280, 87169790, 508887860, 2865204762, 15654301865, 83388235348, 434685964540, 2223970137825, 11194499812388, 55546566721430, 272142754971892, 1318317357277470, 6321681903231990, 30037740651227756, 141545610360126400

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

N. J. A. Sloane

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