A006420 Number of rooted planar maps with 3 vertices and n faces and no isthmuses. (Formerly M5012)

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

Offset

2,2

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

Prog

(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

Crossrefs

A diagonal of A342981.

Sequence in context: A135458 A000486 A223069 * A221422 A049351 A240424

Adjacent sequences: A006417 A006418 A006419 * A006421 A006422 A006423

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

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

Status

approved