%I A057009
%S A057009 1,7,41,235,1361,7987,47321,281995,1685921,10096867,60524201,362972155,
%T A057009 2177309681,13062280147,78368930681,470199300715,2821152888641,
%U A057009 16926788453827,101560343826761,609360901747675,3656161925798801
%N A057009 Number of conjugacy classes of subgroups of index 3 in free group of 
               rank n.
%D A057009 J. H. Kwak and J. Lee, J. Graph Th., 23 (1996), 105-109.
%D A057009 V. A. Liskovets, Reductive enumeration under mutually orthogonal group 
               actions, Acta Applic. Math., 52 (1998), 91-120.
%D A057009 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Problem 5.13(c), pp. 76, 112.
%H A057009 J. H. Kwak and J. Lee, <a href="http://com2mac.postech.ac.kr/resorce/
               Lecture_text.htm">Enumeration of graph coverings and surface branched 
               coverings</a>, Lecture Note Series 1 (2001), Com^2MaC-KOSEF, Korea. 
               See chapter 3.
%F A057009 G.f.: x(1-4x)/((1-2x)(1-3x)(1-6x)). a(n)=6^(n-1)+3^(n-1)-2^(n-1).
%F A057009 E.g.f.: e^(6*x)+e^(3*x)-e^(2*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), 
               Jan 16 2009]
%o A057009 (PARI) a(n)=if(n<0,0,6^(n-1)+3^(n-1)-2^(n-1))
%Y A057009 Cf. A057004-A057013.
%Y A057009 Sequence in context: A097165 A152268 A026002 this_sequence A140480 A002315 
               A141813
%Y A057009 Adjacent sequences: A057006 A057007 A057008 this_sequence A057010 A057011 
               A057012
%K A057009 nonn
%O A057009 1,2
%A A057009 N. J. A. Sloane (njas(AT)research.att.com), Sep 09 2000
%E A057009 More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), 
               Dec 25 2001