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Search: id:A000309
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| A000309 |
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Number of rooted cubic maps with 2n nodes.
(Formerly M3601 N1460)
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+0
7
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| 1, 1, 4, 24, 176, 1456, 13056, 124032, 1230592, 12629760, 133186560, 1436098560, 15774990336, 176028860416, 1990947110912, 22783499599872, 263411369705472, 3073132646563840, 36143187370967040, 428157758086840320
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also counts rooted planar non-separable triangulations with 3n edges. - Valery Liskovets (liskov(AT)im.bas-net.by), Dec 01 2003
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Dulucq and O. Guibert, Stack words, standard tableaux and Baxter permutations, Discr. Math., 157 (1996), 91-106.
R. C. Mullin, On counting rooted triangular maps, Canad. J. Math., v.17 (1965), 373-382.
W. T. Tutte, A census of Hamiltonian polygons, Canad. J. Math., 14 (1962), 402-417.
W. T. Tutte, On the enumeration of four-colored maps, SIAM J. Appl. Math., 17 (1969), 454-460.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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a(n) = 4*a(n-1)*binomial(3n, 3) / binomial(2n+2, 3); a(n) = 2^n*(3*n)!/ ( (n+1)!*(2*n+1)! ).
G.f.: (1/(6*x)) * (hypergeom([ -2/3, -1/3],[1/2],(27/2)*x)-1) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Nov 02 2009]
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MAPLE
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f:=n->2^(n+1)*(3*n)!/(n!*(2*n+2)!);
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MATHEMATICA
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f[n_] := 2^n(3n)!/((n + 1)!(2n + 1)!); Table[f[n], {n, 0, 19}] (from Robert G. Wilson v Sep 21 2004)
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CROSSREFS
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Equals 2^(n-1) * A000139(n) for n>0. Cf. A006335, A000264, A000356.
Sequence in context: A032349 A103334 A156017 this_sequence A112914 A007846 A139702
Adjacent sequences: A000306 A000307 A000308 this_sequence A000310 A000311 A000312
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com) and Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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Definition clarified by Michael Albert, Oct 24 2008
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