A000502 Number of genus 0 rooted maps with 6 faces and n vertices. (Formerly M5280 N2298)

42, 1586, 31388, 442610, 5030004, 49145460, 429166584, 3435601554, 25658464260, 181055975100, 1218601601672, 7880146275092, 49238911113224, 298652277299880, 1764885293279472, 10192638073849554, 57674223198273444, 320430129184331628, 1751190732477786600, 9428906326013866076

Offset

5,1

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.

Links

Andrew Howroyd, Table of n, a(n) for n = 5..500

W. T. Tutte, On the enumeration of planar maps, Bull. Amer. Math. Soc. 74 1968 64-74.

T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus, J. Comb. Thy B13 (1972), 122-141 and 192-218.

Notes

Formula

G.f.: x^4*(1-sqrt(1-4*x))*(105+92*x-(84+76*x)*sqrt(1-4*x))/(1-4*x)^7. - Sean A. Irvine, Nov 14 2010

Mathematica

CoefficientList[ x(1-Sqrt[1-4x])(105+92x-(84+76x)Sqrt[1-4x])/(1-4x)^7/x^2 + O[x]^30, x] (* Jean-François Alcover, Feb 09 2016 *)

Prog

(PARI) seq(n)={my(g=sqrt(1-4*x + O(x*x^n))); Vec((1-g)*(105+92*x - (84+76*x)*g)/((1-4*x)^7))} \\ Andrew Howroyd, Mar 28 2021

Crossrefs

Column 6 of A269920.

Column 0 of A270410.

Sequence in context: A067638 A155021 A270410 * A215545 A004997 A120815

Adjacent sequences: A000499 A000500 A000501 * A000503 A000504 A000505

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 14 2010

Status

approved