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

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

Offset

2,1

Comments

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

Links

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.

Formula

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

Mathematica

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 *)

Prog

(PARI) 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

Crossrefs

Cf. A038787.

Sequence in context: A309718 A230814 A325502 * A327563 A326950 A001696

Adjacent sequences: A038788 A038789 A038790 * A038792 A038793 A038794

Keyword

nonn,easy

Author

N. J. A. Sloane, May 04 2000

Extensions

More terms from Valery A. Liskovets, May 09 2001

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

Status

approved