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A270785 Number of Schur rings over Z_{3^n}. 4
1, 2, 7, 25, 92, 345, 1311, 5030, 19439, 75545, 294888, 1155205, 4538745, 17876250, 70553179, 278949705, 1104585634, 4379770585, 17386456213, 69090680674, 274806384941, 1093933313537, 4357881016922, 17371974200097, 69292334180593, 276541159696582 (list; graph; refs; listen; history; text; internal format)
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 + (1-x)*sqrt(1-4*x)); equivalently, the g.f. can be rewritten as -y^2*(y^2 - y + 1)/(y^4 - 3*y^3 + 4*y^2 - 4*y + 1), where y=A000108(x). - Gheorghe Coserea, Sep 10 2018

MATHEMATICA

om[n_] := om[n] = x om[n - 1] + Sum[(CatalanNumber[k - 1] x + 1) om[n - k], {k, 2, n}] // Expand; om[0] = 1; om[1] = x;

Array[om, 26, 0] /. x -> 2 (* Jean-Fran├žois Alcover, Oct 25 2018 *)

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(2)) \\ Gheorghe Coserea, Sep 10 2018

CROSSREFS

Cf. A000108, A269750.

Sequence in context: A074605 A292613 A108081 * A199247 A242728 A116396

Adjacent sequences:  A270782 A270783 A270784 * A270786 A270787 A270788

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

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Last modified February 19 10:13 EST 2019. Contains 320310 sequences. (Running on oeis4.)