A006420 Number of rooted planar maps with 3 vertices and n faces and no isthmuses.

1, 16, 150, 1104, 7077, 41504, 228810, 1205520, 6135690, 30391520, 147277676, 700990752, 3286733805, 15215673408, 69675615234, 316058238864, 1421891923038, 6350464644960, 28179908990772, 124327908683616, 545691921346146, 2383936774151616, 10370479696102500

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 and 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 + 2*g - 4*g^2)/((1 - g)^4*(1 - 2*g)^5))} \\ Andrew Howroyd, Apr 06 2021

Formula

G.f.: x^2*(1 + 2*g - 4*g^2)/((1 - g)^4*(1 - 2*g)^5) where g/x is the g.f. of A000108.

Extensions

a(14) and a(15) from Sean A. Irvine, Apr 05 2017

Terms a(16) and beyond from Andrew Howroyd, Apr 02 2021