A006421 Number of rooted planar maps with 4 vertices and n faces and no isthmuses.

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

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

A diagonal of A342981.

Programs

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

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

Extensions

a(13) and title improved by Sean A. Irvine, Apr 06 2017

Terms a(14) and beyond from Andrew Howroyd, Apr 02 2021