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 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), 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 (9,-20,12). FORMULA a(n) = 3*6^n-3*2^n+1. G.f.: (1+4*x)/((1-x)*(1-2*x)*(1-6*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 EXTENSIONS More terms from Karen Richardson (s1149414(AT)cedarville.edu) STATUS approved

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Last modified September 15 20:11 EDT 2019. Contains 327086 sequences. (Running on oeis4.)