3,2

Number of inequivalent undirected Hamiltonian cycles in complete graph on n labeled nodes under action of dihedral group of order 2n acting on nodes.

S. W. Golomb and L. R. Welch, On the enumeration of polygons, Amer. Math. Monthly, 67 (1960), 349-353.

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]

E. M. Palmer and R. W. Robinson, Enumeration under two representations of the wreath product, Acta Math., 131 (1973), 123-143.

R. C. Read, Combinatorial problems in theory of music, Discrete Math. 167 (1997), 543-551.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=3..100

For formula see Maple lines.

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;

# 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;

Cf. A000939. Bisections give A094156, A094157.

Sequence in context: A149845 A149846 A108532 this_sequence A008404 A099214 A126946

Adjacent sequences: A000937 A000938 A000939 this_sequence A000941 A000942 A000943

nonn,easy,nice,new

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 05 2004