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A000309
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Number of rooted cubic maps with 2n nodes.
(Formerly M3601 N1460)
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| S. Dulucq and O. Guibert, Stack words, standard tableaux and Baxter permutations, Discr. Math., 157 (1996), 91-106.
C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979.
R. C. Mullin, On counting rooted triangular maps, Canad. J. Math., v.17 (1965), 373-382.
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 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
| T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
| 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
| f:=n->2^(n+1)*(3*n)!/(n!*(2*n+2)!);
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MATHEMATICA
| f[n_] := 2^n(3n)!/((n + 1)!(2n + 1)!); Table[f[n], {n, 0, 19}] (from Robert G. Wilson v Sep 21 2004)
Join[{1}, RecurrenceTable[{a[1]==1, a[n]==4a[n-1] Binomial[3n, 3]/ Binomial[2n+2, 3]}, a[n], {n, 20}]] (* From Harvey P. Dale, May 11 2011 *)
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CROSSREFS
| Equals 2^(n-1) * A000139(n) for n>0. Cf. A006335, A000264, A000356.
Sequence in context: A032349 A103334 A156017 * A112914 A007846 A139702
Adjacent sequences: A000306 A000307 A000308 * A000310 A000311 A000312
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
| Definition clarified by Michael Albert, Oct 24 2008
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