A049295 Number of subgroups of index 4 in free group of rank n+1.

1, 71, 2143, 54335, 1321471, 31817471, 764217343, 18344733695, 440294408191, 10567189327871, 253613279903743, 6086723113107455, 146081381003558911, 3505953301484470271, 84142880178680889343, 2019429129941297135615, 48466299152487396933631

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 A332665 A017734

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