|
Search: id:A000309
|
|
|
| A000309 |
|
Number of rooted maps with 2n nodes.
(Formerly M3601 N1460)
|
|
+0
5
|
|
| 1, 1, 4, 24, 176, 1456, 13056, 124032, 1230592, 12629760, 133186560, 1436098560, 15774990336, 176028860416, 1990947110912, 22783499599872, 263411369705472, 3073132646563840, 36143187370967040, 428157758086840320
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Also counts rooted planar non-separable triangulations with 3n edges. - Valery Liskovets (liskov(AT)im.bas-net.by), Dec 01 2003
|
|
REFERENCES
|
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.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..100
|
|
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)! ).
|
|
MAPLE
|
f:=n->2^(n+1)*(3*n)!/(n!*(2*n+2)!);
|
|
MATHEMATICA
|
f[n_] := 2^n(3n)!/((n + 1)!(2n + 1)!); Table[f[n], {n, 0, 19}] (from Robert G. Wilson v Sep 21 2004)
|
|
CROSSREFS
|
Equals 2^(n-1) * A000139(n) for n>0. Cf. A006335.
Sequence in context: A052685 A032349 A103334 this_sequence A112914 A007846 A139702
Adjacent sequences: A000306 A000307 A000308 this_sequence A000310 A000311 A000312
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
njas, Robert G. Wilson v (rgwv(AT)rgwv.com)
|
|
|
Search completed in 0.002 seconds
|
