[go: up one dir, main page]

login
A000473
Number of genus 0 rooted maps with 5 faces and n vertices.
(Formerly M4953 N2122)
2
14, 386, 5868, 65954, 614404, 5030004, 37460376, 259477218, 1697186964, 10596579708, 63663115880, 370293754740, 2095108370600, 11574690111400, 62629794691632, 332742342741090, 1739371969822260, 8961709528660140, 45576855706440520, 229087231033907708
OFFSET
4,1
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
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.
FORMULA
G.f.: x^3*(1-sqrt(1-4*x))*(17+16*x-(10+4*x)*sqrt(1-4*x))/(1-4*x)^(11/2). - Sean A. Irvine, Nov 14 2010
MATHEMATICA
CoefficientList[(1/x)(1-Sqrt[1-4x])(17+16x-(10+4x)Sqrt[1-4x])/(1-4x)^(11/2) + O[x]^36, x] (* Jean-François Alcover, Feb 08 2016 *)
PROG
(PARI) seq(n)={my(g=sqrt(1-4*x + O(x*x^n))); Vec((1-g)*(17+16*x-(10+4*x)*g)/((1-4*x)^5*g))} \\ Andrew Howroyd, Mar 28 2021
CROSSREFS
Column 5 of A269920.
Column 0 of A270409.
Sequence in context: A159535 A171718 A270409 * A233094 A211421 A097310
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Nov 14 2010
STATUS
approved