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A000287
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Number of rooted polyhedral graphs with n edges.
(Formerly M3290 N1326)
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1
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1, 0, 4, 6, 24, 66, 214, 676, 2209, 7296, 24460, 82926, 284068, 981882, 3421318, 12007554, 42416488, 150718770, 538421590, 1932856590, 6969847486, 25237057110, 91729488354, 334589415276, 1224445617889, 4494622119424
(list; graph; refs; listen; history; internal format)
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OFFSET
| 6,3
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REFERENCES
| A. J. W. Duijvestijn and P. J. Federico, The number of polyhedral (3-connected planar) graphs. Math. Comp. 37 (1981), no. 156, 523-532.
Handbook of Combinatorics, North-Holland '95, p. 892. (Gives different last term)
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 new branch of enumerative graph theory, Bull. Amer. Math. Soc., 68 (1962), 500-504.
W. T. Tutte, A census of planar maps, Canad. J. Math., 15 (1963), 249-271.
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FORMULA
| a(n) = b(n-1) + 2*(-1)^n, n>=4, where b(3)=2, b(n) = [2*(2*n)!/(n!)^2 - (27*n^2+9*n-2)b(n-1)] / (54*n^2-90*n+32). [From Sean A. Irvine (sairvin(AT)xtra.co.nz), Apr 14 2010]
(n + 4) a(n) = (3/2 n - 3) a(n - 1) + (8 n + 4) a(n - 2) + (15/2 n + 6) a(n - 3) + (2 n + 3) a(n - 4) [From Simon Plouffe, Feb 09 2012]
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MATHEMATICA
| a[6] = 1; a[n_] := a[n] = ((9*(5 - 3*n)*n - 16)*a[n-1]*((n-1)!)^2 + 2*((-1)^n*(9*n*(3*n - 17) + 160)*((n-1)!)^2 + ((2*n - 2)!)))/(2*(9*n*(3*n - 11) + 88)*((n-1)!)^2); Table[ a[n], {n, 6, 31}] (* From Jean-François Alcover, Oct 04 2011, after formula *)
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CROSSREFS
| Cf. A000256.
Sequence in context: A034458 A067001 A057343 * A032087 A165164 A136591
Adjacent sequences: A000284 A000285 A000286 * A000288 A000289 A000290
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KEYWORD
| nonn,nice,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Apr 14 2010
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