A002087 -id:A002087 - cp's OEIS frontend

A049288 Number of nonisomorphic circulant tournaments, i.e., Cayley tournaments for cyclic group of order 2n-1.

1, 1, 1, 2, 3, 4, 6, 16, 16, 30, 88, 94, 205, 457, 586, 1096, 3280, 5472, 7286, 21856, 26216, 49940, 174848, 182362, 399472, 1048576, 1290556, 3355456, 7456600, 9256396, 17895736, 59654816, 89478656, 130150588, 390451576, 490853416, 954437292

Offset: 1

Valery A. Liskovets

Further values for prime-squared orders can be found in A038789.

There is an easy formula for prime orders. Formulae are also known for squarefree and prime-squared orders.

B. Alspach, On point-symmetric tournaments, Canad. Math. Bull., 13 (1970), 317-323. [Annotated copy] See r(n).
B. Alspach, On point-symmetric tournaments, Canad. Math. Bull., 13 (1970), 317-323. See r(n).
V. A. Liskovets, Some identities for enumerators of circulant graphs, arXiv:math/0104131 [math.CO], 2001.
V. A. Liskovets and R. Poeschel, On the enumeration of circulant graphs of prime-power and squarefree orders
R. Poeschel, Publications
Index entries for sequences related to tournaments

Cf. A002086, A002087, A038789, A049297, A049287, A049289, A060966.

a(n) <= A002086(n). - Andrew Howroyd, Apr 28 2017

a(n) = A002086(n) for squarefree 2n-1. - Andrew Howroyd, Apr 28 2017

a(14)-a(37) from Andrew Howroyd, Apr 28 2017

Reference to Alspach (1970) corrected by Andrew Howroyd, Apr 28 2017

A002086 Number of circulant tournaments on 2n+1 nodes up to Cayley isomorphism.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

nonn

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).

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

Cf. A002087, A049288.

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 *)

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;
IsBidrected(s,r,f)={my(t=f(s));while(t<>s&&t<>r,t=f(t));t==r}
IsC(n,k)=sum(u=1,n-1,IsBidrected(u,n-u,v->v*k%n))==0;
a(n)=my(m=2*n+1);sum(k=1, m, if (gcd(m,k)==1 && IsC(m,k), 2^C(m,k),0))/eulerphi(m); \\ Andrew Howroyd, Sep 30 2017

More terms from Roderick J. Fletcher, Oct 15 1996 (yylee(AT)mail.ncku.edu.tw)
Definition corrected by Andrew Howroyd, Apr 28 2017
Terms a(32) and beyond from Andrew Howroyd, Sep 30 2017

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A049288 Number of nonisomorphic circulant tournaments, i.e., Cayley tournaments for cyclic group of order 2n-1.

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A002086 Number of circulant tournaments on 2n+1 nodes up to Cayley isomorphism.

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