%I A000309 M3601 N1460
%S A000309 1,1,4,24,176,1456,13056,124032,1230592,12629760,133186560,1436098560,
%T A000309 15774990336,176028860416,1990947110912,22783499599872,263411369705472,
%U A000309 3073132646563840,36143187370967040,428157758086840320
%N A000309 Number of rooted cubic maps with 2n nodes.
%C A000309 Also counts rooted planar non-separable triangulations with 3n edges. 
               - Valery Liskovets (liskov(AT)im.bas-net.by), Dec 01 2003
%D A000309 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000309 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000309 S. Dulucq and O. Guibert, Stack words, standard tableaux and Baxter permutations, 
               Discr. Math., 157 (1996), 91-106.
%D A000309 R. C. Mullin, On counting rooted triangular maps, Canad. J. Math., v.17 
               (1965), 373-382.
%D A000309 W. T. Tutte, A census of Hamiltonian polygons, Canad. J. Math., 14 (1962), 
               402-417.
%D A000309 W. T. Tutte, On the enumeration of four-colored maps, SIAM J. Appl. Math., 
               17 (1969), 454-460.
%H A000309 T. D. Noe, <a href="b000309.txt">Table of n, a(n) for n=0..100</a>
%F A000309 a(n) = 4*a(n-1)*binomial(3n, 3) / binomial(2n+2, 3); a(n) = 2^n*(3*n)!/ 
               ( (n+1)!*(2*n+1)! ).
%F A000309 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]
%p A000309 f:=n->2^(n+1)*(3*n)!/(n!*(2*n+2)!);
%t A000309 f[n_] := 2^n(3n)!/((n + 1)!(2n + 1)!); Table[f[n], {n, 0, 19}] (from 
               Robert G. Wilson v Sep 21 2004)
%Y A000309 Equals 2^(n-1) * A000139(n) for n>0. Cf. A006335, A000264, A000356.
%Y A000309 Sequence in context: A032349 A103334 A156017 this_sequence A112914 A007846 
               A139702
%Y A000309 Adjacent sequences: A000306 A000307 A000308 this_sequence A000310 A000311 
               A000312
%K A000309 nonn,nice
%O A000309 0,3
%A A000309 N. J. A. Sloane (njas(AT)research.att.com) and Robert G. Wilson v (rgwv(AT)rgwv.com)
%E A000309 Definition clarified by Michael Albert, Oct 24 2008