A270787 Number of Schur rings over Z_{7^n}.

1, 4, 21, 113, 614, 3351, 18329, 100372, 550009, 3015021, 16531326, 90653323, 497159809, 2726660260, 14954795741, 82023673921, 449887538266, 2467587944471, 13534552583013, 74236396347076, 407184278878261, 2233396783681309, 12250146572763594, 67191916861119507, 368547111683611193

Offset

0,2

Links

Gheorghe Coserea, Table of n, a(n) for n = 0..1001

Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757 [math.RA], 2015.

Formula

G.f.: (1-x)/(-x^2 + x-1 + 2*(1-x)*sqrt(1-4*x)); equivalently, the g.f. can be rewritten as -y^2*(y^2 - y + 1)/(3*y^4 - 7*y^3 + 8*y^2 - 6*y + 1), where y=A000108(x). - Gheorghe Coserea, Sep 10 2018

Mathematica

c[k_] := Binomial[2k, k]/(k+1);
om[0, _] = 1; om[1, x_] := x; om[n_, x_] := om[n, x] = x om[n-1, x] + Sum[ (c[k-1] x + 1) om[n-k, x], {k, 2, n}];
Table[om[n, 4], {n, 0, 25}] (* Jean-François Alcover, Oct 05 2018, after Gheorghe Coserea *)

Prog

(PARI)
A269750_seq(N, t='t) = {
  my(a=vector(N), c(k)=binomial(2*k, k)/(k+1)); a[1]=1; a[2]=t;
  for (n = 2, N-1,
    a[n+1] = t*a[n] + sum(k = 2, n, (c(k-1)*t+1)*a[n+1-k]));
  return(a);
};
A269750_seq(25, numdiv(6)) \\ Gheorghe Coserea, Sep 10 2018

Crossrefs

Cf. A000108, A269750.

Sequence in context: A026335 A027909 A127111 * A190089 A349300 A240436

Adjacent sequences: A270784 A270785 A270786 * A270788 A270789 A270790

Keyword

nonn

Author

N. J. A. Sloane, Mar 23 2016

Extensions

More terms from Gheorghe Coserea, Mar 24 2016

a(0)=1 prepended by Gheorghe Coserea, Sep 10 2018

Status

approved