A038789 -id:A038789 - 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

A038785 Number of nonisomorphic circulant self-complementary directed p^2-graphs, indexed by odd primes p.

Original entry on oeis.org

3, 214, 399472, 10481104587335128, 123992391755402970674764, 81988033818127290961563099285346969398730, 4480981113642949878240780781141254929604041319893664

Offset: 1

N. J. A. Sloane, May 04 2000

a(p^2)=A038789(p^2) for p=4k-1

Farrugia, Alastair; Self-complementary graphs and generalizations: a comprehensive reference, M.Sc. Thesis, University of Malta, August 1999. See p. 198.
M. Klin, V. A. Liskovets and R. Poeschel, Analytical enumeration of circulant graphs with prime-squared vertices, Sem. Lotharingien de Combin., B36d, 1996, 36 pages.

Cf. A049309.

More terms from Valery A. Liskovets, May 09 2001

A038791 An intermediate sequence for nonisomorphic circulant p^2-tournaments, indexed by odd primes p.

Original entry on oeis.org

2, 4, 12, 104, 344, 4096, 14572, 190652, 9586984, 35791472, 1908874584, 27487790720, 104715393912, 1529755308212, 86607685141744, 4969489243995032, 19215358410149344, 1117984489315857512, 16865594581677305360, 65588423373189982912

Offset: 2

N. J. A. Sloane, May 04 2000

Number of subsets of {1, ..., p} with product = 1 mod p, where p is the n-th prime. - Charles R Greathouse IV, Jun 06 2013

Also : Number of subsets of {1, ..., p} with product = -1 mod p, where p is the n-th prime. - Ridouane Oudra, Jul 08 2025

Charles R Greathouse IV, Table of n, a(n) for n = 2..100
M. Klin, V. A. Liskovets and R. Poeschel, Analytical enumeration of circulant graphs with prime-squared vertices, Sem. Lotharingien de Combin., B36d, 1996, 36 pages.

Cf. A038787, A238446.

has[p_] := Module[{v, u}, v = Table[0, {p-1}]; v[[1]] = 1; For[n = 2, n <= p-1, n++, u = Table[0, {p-1}]; For[j = 1, j <= p-1, j++, u[[Mod[j*n, p]]] += v[[j]]]; v += u]; 2*v[[1]]];
a[n_] := has[Prime[n]];
Table[a[n], {n, 2, 21}] (* Jean-François Alcover, Aug 30 2019, after Charles R Greathouse IV *)

has(p)=my(v=vector(p-1),u); v[1]=1; for(n=2,p-1,u=vector(p-1); for(j=1,p-1, u[j*n%p]+=v[j]);v+=u); 2*v[1]
a(n)=has(prime(n)) \\ Charles R Greathouse IV, Jun 06 2013

a(p^2) = A038790(p^2) - A038789(p^2) + A038792(p^2).

a(n) = A238446(n) + 1. - Ridouane Oudra, Jul 08 2025

More terms from Valery A. Liskovets, May 09 2001

a(12)-a(20) from Charles R Greathouse IV, Jun 06 2013

A038790 Circulant p^2-tournaments up to rotations only, indexed by odd primes p.

Original entry on oeis.org

4, 208, 399480, 10481104587335216, 123992391755346585462944, 81988033818127290961528376002383682011136, 4480981113642949878240780781141254929604041319907336

Offset: 1

N. J. A. Sloane, May 04 2000

M. Klin, V. A. Liskovets and R. Poeschel, Analytical enumeration of circulant graphs with prime-squared vertices, Sem. Lotharingien de Combin., B36d, 1996, 36 pages.

Cf. A038786, A038789.

More terms from Valery A. Liskovets, May 09 2001

Offset corrected by Sean A. Irvine, Feb 14 2021

cp's OEIS Frontend

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

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A038785 Number of nonisomorphic circulant self-complementary directed p^2-graphs, indexed by odd primes p.

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A038791 An intermediate sequence for nonisomorphic circulant p^2-tournaments, indexed by odd primes p.

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A038790 Circulant p^2-tournaments up to rotations only, indexed by odd primes p.

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