|
| |
|
|
A000256
|
|
Number of simple triangulations of plane with n nodes.
(Formerly M2923 N1173)
|
|
3
| |
|
|
1, 1, 0, 1, 3, 12, 52, 241, 1173, 5929, 30880, 164796, 897380, 4970296, 27930828, 158935761, 914325657, 5310702819, 31110146416, 183634501753, 1091371140915, 6526333259312, 39246152584304, 237214507388796, 1440503185260748
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 3,5
|
|
|
REFERENCES
| S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, < a href="http://arxiv.org/ftp/arxiv/papers/0912/0912.0072.pdf"> Une méthode pour obtenir la fonction génératrice d'une série. FPSAC 1993, Florence. Formal Power Series and Algebraic Combinatorics.
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).
W. T. Tutte, A census of planar triangulations, Canad. J. Math., 14 (1962), 21-38.
W. T. Tutte, A census of planar maps, Canad. J. Math., 15 (1963), 249-271.
W. T. Tutte, The enumerative theory of planar maps, pp. 437-448 of J. N. Srivastava, ed., A Survey of Combinatorial Theory, North-Holland, 1973.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=3..200
|
|
|
FORMULA
| a(n) = (1/4)*(7*binomial(3*n-9, n-4)-(8*n^2-43*n+57)*a(n-1))/(8*n^2-51*n+81), n>4. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 19 2004
(1/4 + 7/8*n - 9/8*n^3)*a(n) + (-5/4 + 2/3*n + 59/12*n^2 - 13/3*n^3)*a(n+1) + (-1 - 2/3*n + n^2 + 2/3*n^3)*a(n+2). [Simon Plouffe, Feb 09 2012]
|
|
|
MAPLE
| R := RootOf(x-t*(t-1)^2, t); ogf := series( (2*R^3+2*R^2-2*R-1)/((R-1)*(R+1)^2), x=0, 20); - Mark van Hoeij, Nov 08 2011
|
|
|
CROSSREFS
| Sequence in context: A010736 A151197 A007198 * A124202 A138269 A151198
Adjacent sequences: A000253 A000254 A000255 * A000257 A000258 A000259
|
|
|
KEYWORD
| nonn,nice,changed
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 19 2004
|
| |
|
|
