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A057009
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Number of conjugacy classes of subgroups of index 3 in free group of rank n.
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0
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1, 7, 41, 235, 1361, 7987, 47321, 281995, 1685921, 10096867, 60524201, 362972155, 2177309681, 13062280147, 78368930681, 470199300715, 2821152888641, 16926788453827, 101560343826761, 609360901747675, 3656161925798801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| J. H. Kwak and J. Lee, J. Graph Th., 23 (1996), 105-109.
V. A. Liskovets, Reductive enumeration under mutually orthogonal group actions, Acta Applic. Math., 52 (1998), 91-120.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(c), pp. 76, 112.
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LINKS
| J. H. Kwak and J. Lee, Enumeration of graph coverings and surface branched coverings, Lecture Note Series 1 (2001), Com^2MaC-KOSEF, Korea. See chapter 3.
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FORMULA
| G.f.: x(1-4x)/((1-2x)(1-3x)(1-6x)). a(n)=6^(n-1)+3^(n-1)-2^(n-1).
E.g.f.: e^(6*x)+e^(3*x)-e^(2*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), Jan 16 2009]
a(1)=1, a(2)=7, a(3)=41, a(n)=11*a(n-1)-36*a(n-2)+36*a(n-3) [From Harvey P. Dale, Nov 24 2011]
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MATHEMATICA
| Table[6^(n-1)+3^(n-1)-2^(n-1), {n, 25}] (* or *) LinearRecurrence[ {11, -36, 36}, {1, 7, 41}, 25] (* From Harvey P. Dale, Nov 24 2011 *)
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PROG
| (PARI) a(n)=if(n<0, 0, 6^(n-1)+3^(n-1)-2^(n-1))
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CROSSREFS
| Cf. A057004-A057013.
Sequence in context: A152268 A026002 A173409 * A140480 A002315 A141813
Adjacent sequences: A057006 A057007 A057008 * A057010 A057011 A057012
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Sep 09 2000
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EXTENSIONS
| More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 25 2001
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