|
| |
|
|
A049294
|
|
Number of subgroups of index 3 in free group of rank n+1.
|
|
3
| |
|
|
1, 13, 97, 625, 3841, 23233, 139777, 839425, 5038081, 30231553, 181395457, 1088385025, 6530334721, 39182057473, 235092443137, 1410554855425, 8463329525761, 50779977940993, 304679869218817, 1828079218458625
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| M. Hall, Subgroups of finite index in free groups, Canad. J. Math., 1 (1949), 187-190.
P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 23.
V. A. Liskovets and A. Mednykh, Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces, Commun. in Algebra, 28, No. 4 (2000), 1717-1738.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(b).
|
|
|
FORMULA
| a(n)=3*6^n-3*2^n+1.
|
|
|
CROSSREFS
| Cf. A003319, A027837, A049290-A049295.
Sequence in context: A141894 A160554 A125350 * A198480 A126508 A158795
Adjacent sequences: A049291 A049292 A049293 * A049295 A049296 A049297
|
|
|
KEYWORD
| easy,nice,nonn
|
|
|
AUTHOR
| V. A. Liskovets (liskov(AT)im.bas-net.by)
|
|
|
EXTENSIONS
| More terms from Karen Richardson (s1149414(AT)cedarville.edu)
|
| |
|
|
