

A049294


Number of subgroups of index 3 in free group of rank n+1.


5



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;
text;
internal format)



OFFSET

0,2


REFERENCES

P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 23.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(b).


LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000
M. Hall, Subgroups of finite index in free groups, Canad. J. Math., 1 (1949), 187190.
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), 17171738.
Index entries for linear recurrences with constant coefficients, signature (9,20,12).


FORMULA

a(n) = 3*6^n3*2^n+1.
G.f.: (1+4*x)/((1x)*(12*x)*(16*x)). [Colin Barker, May 08 2012]


MATHEMATICA

LinearRecurrence[{9, 20, 12}, {1, 13, 97}, 20] (* Harvey P. Dale, Sep 24 2017 *)


CROSSREFS

Cf. A003319, A027837, A049290, A049291, A049292, A049293, A049295.
Sequence in context: A160554 A211388 A125350 * A198480 A126508 A228680
Adjacent sequences: A049291 A049292 A049293 * A049295 A049296 A049297


KEYWORD

easy,nice,nonn


AUTHOR

Valery A. Liskovets


EXTENSIONS

More terms from Karen Richardson (s1149414(AT)cedarville.edu)


STATUS

approved



