A002086 - OEIS

A002086

Number of circulant tournaments on 2n+1 nodes up to Cayley isomorphism.
(Formerly M0939 N0353)

1, 1, 2, 4, 4, 6, 16, 16, 30, 88, 94, 208, 472, 586, 1096, 3280, 5472, 7286, 21856, 26216, 49940, 175104, 182362, 399480, 1048576, 1290556, 3355456, 7456600, 9256396, 17895736, 59660288, 89478656, 130150588, 390451576, 490853416, 954437292, 3435974656

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

REFERENCES

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).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

B. Alspach, On point-symmetric tournaments, Canad. Math. Bull., 13 (1970), 317-323. See g(n) as defined on page 322 (NOT on page 317).

B. Alspach, On point-symmetric tournaments, Canad. Math. Bull., 13 (1970), 317-323. [Annotated copy] See g(n) as defined on page 322 (NOT on page 317).

Index entries for sequences related to tournaments

MATHEMATICA

IsLeastPoint[s_, f_] := Module[{t = f[s]}, While[t > s, t = f[t]]; s == t];

C0[n_, k_] := Sum[Boole @ IsLeastPoint[u, Mod[#*k, n]&], {u, 1, n-1}]/2;

IsBidrected[s_, r_, f_] := Module[{t = f[s]}, While[t != s && t != r, t = f[t]]; t == r];

IsC[n_, k_] := Sum[Boole @ IsBidrected[u, n-u, Mod[#*k, n]&], {u, 1, n-1}] == 0;

a[n_] := Module[{m = 2*n + 1}, Sum[If [GCD[m, k] == 1 && IsC[m, k], 2^C0[m, k], 0], {k, 1, m}]/EulerPhi[m]];

Array[a, 40] (* Jean-François Alcover, Jul 02 2018, after Andrew Howroyd *)

PROG

(PARI)

IsLeastPoint(s, f)={my(t=f(s)); while(t>s, t=f(t)); s==t}

C(n, k)=sum(u=1, n-1, IsLeastPoint(u, v->v*k%n))/2;