|
| |
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
Andrew Howroyd, Table of n, a(n) for n = 4..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^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
Adjacent sequences: A000470 A000471 A000472 * A000474 A000475 A000476
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
EXTENSIONS
|
More terms from Sean A. Irvine, Nov 14 2010
|
|
|
STATUS
|
approved
|
| |
|
|
