login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A049295 Number of subgroups of index 4 in free group of rank n+1. 6
1, 71, 2143, 54335, 1321471, 31817471, 764217343, 18344733695, 440294408191, 10567189327871, 253613279903743, 6086723113107455, 146081381003558911, 3505953301484470271, 84142880178680889343, 2019429129941297135615, 48466299152487396933631 (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, N_{4,n}.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(b).

LINKS

Table of n, a(n) for n=0..16.

M. Hall, Subgroups of finite index in free groups, Canad. J. Math., 1 (1949), 187-190.

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.

Index entries for linear recurrences with constant coefficients, signature (37,-368,1436,-2256,1152).

FORMULA

a(n) = 4*24^n-4*6^n-2*4^n+4*2^n-1.

G.f.: (264*x^3+116*x^2-34*x-1) / ((x-1)*(2*x-1)*(4*x-1)*(6*x-1)*(24*x-1)). [Colin Barker, Feb 17 2013]

MATHEMATICA

LinearRecurrence[{37, -368, 1436, -2256, 1152}, {1, 71, 2143, 54335, 1321471}, 20] (* Harvey P. Dale, Apr 14 2016 *)

CROSSREFS

Cf. A003319, A027837, A049290-A049294.

Sequence in context: A093271 A201608 A225741 * A017787 A017734 A263248

Adjacent sequences:  A049292 A049293 A049294 * A049296 A049297 A049298

KEYWORD

nonn,easy,nice

AUTHOR

Valery A. Liskovets

EXTENSIONS

More terms from Carrie Westbrook (s1213407(AT)cedarville.edu)

Terms corrected by Colin Barker, May 08 2012

a(16) from Colin Barker, Feb 17 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 23 04:57 EST 2018. Contains 299473 sequences. (Running on oeis4.)