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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, 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 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 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

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Last modified January 26 14:08 EST 2020. Contains 331280 sequences. (Running on oeis4.)