Search: id:A000940
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%I A000940 M1260 N0482
%S A000940 1,2,4,12,39,202,1219,9468,83435,836017,9223092,111255228,1453132944,20433309147,
%T A000940 307690667072,4940118795869,84241805734539,1520564059349452,28963120073957838,
%U A000940 580578894859915650,12217399235411398127,269291841184184374868,6204484017822892034404
%N A000940 Number of n-gons.
%C A000940 Number of inequivalent undirected Hamiltonian cycles in complete graph 
               on n labeled nodes under action of dihedral group of order 2n acting 
               on nodes.
%D A000940 S. W. Golomb and L. R. Welch, On the enumeration of polygons, Amer. Math. 
               Monthly, 67 (1960), 349-353.
%D A000940 J. H. Kwak and J. Lee, Enumeration of graph coverings, surface branched 
               coverings and related group theory, in Combinatorial and Computational 
               Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, 
               Singapore 2001, pp. 97-161. [Added by njas, Nov 12 2009]
%D A000940 E. M. Palmer and R. W. Robinson, Enumeration under two representations 
               of the wreath product, Acta Math., 131 (1973), 123-143.
%D A000940 R. C. Read, Combinatorial problems in theory of music, Discrete Math. 
               167 (1997), 543-551.
%D A000940 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000940 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000940 T. D. Noe, <a href="b000940.txt">Table of n, a(n) for n=3..100</a>
%F A000940 For formula see Maple lines.
%p A000940 with(numtheory); # for n odd: Sd:=proc(n) local t1,d; t1:=2^((n-1)/2)*n^2*((n-1)/
               2)!; for d from 1 to n do if n mod d = 0 then t1:=t1+phi(n/d)^2*d!*(n/
               d)^d; fi; od: t1/(4*n^2); end;
%p A000940 # for n even: Se:=proc(n) local t1,d; t1:=2^(n/2)*n*(n+6)*(n/2)!/4; for 
               d from 1 to n do if n mod d = 0 then t1:=t1+phi(n/d)^2*d!*(n/d)^d; 
               fi; od: t1/(4*n^2); end; A000940:=n-> if n mod 2 = 0 then Se(n) else 
               Sd(n); fi;
%Y A000940 Cf. A000939. Bisections give A094156, A094157.
%Y A000940 Sequence in context: A149845 A149846 A108532 this_sequence A008404 A099214 
               A126946
%Y A000940 Adjacent sequences: A000937 A000938 A000939 this_sequence A000941 A000942 
               A000943
%K A000940 nonn,easy,nice,new
%O A000940 3,2
%A A000940 N. J. A. Sloane (njas(AT)research.att.com).
%E A000940 More terms from Pab Ter (pabrlos(AT)yahoo.com), May 05 2004

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