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A049295 Number of subgroups of index 4 in free group of rank n+1. 6
1, 71, 2143, 54335, 1321471, 31817471, 764217343, 31817471, 764217343, 18344733695, 440294408191, 10567189327871, 253613279903743, 6086723113107455, 146081381003558911, 3505953301484470271, 84142880178680889343, 2019429129941297135615 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

REFERENCES

P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 23, N_{4,n}.

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.

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

FORMULA

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

CROSSREFS

Cf. A003319, A027837, A049290-A049294.

Sequence in context: A198449 A093271 A201608 * A017787 A017734 A115447

Adjacent sequences:  A049292 A049293 A049294 * A049296 A049297 A049298

KEYWORD

easy,nonn,nice

AUTHOR

V. A. Liskovets (liskov(AT)im.bas-net.by)

EXTENSIONS

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

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Last modified February 16 12:41 EST 2012. Contains 205909 sequences.