login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A113788 Number of irreducible multiple zeta values at weight n. 8
0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 7, 8, 11, 13, 17, 21, 28, 34, 45, 56, 73, 92, 120, 151, 197, 250, 324, 414, 537, 687, 892, 1145, 1484, 1911, 2479, 3196, 4148, 5359, 6954, 9000, 11687, 15140, 19672, 25516, 33166, 43065, 56010, 72784, 94716, 123185 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

n * a(n) is the Möbius transform of the Perrin sequence A001608.

Number of unlabeled (i.e., defined up to a rotation) maximal independent sets of the n-cycle graph having n isomorphic representatives. - Jean-Luc Marichal (jean-luc.marichal(AT)uni.lu), Jan 24 2007

LINKS

Danny Rorabaugh, Table of n, a(n) for n = 1..8000

Kam Cheong Au, Evaluation of one-dimensional polylogarithmic integral, with applications to infinite series, arXiv:2007.03957 [math.NT], 2020. See 1st line of Table 1 (p. 6).

R. Bisdorff and J.-L. Marichal, Counting non-isomorphic maximal independent sets of the n-cycle graph, arXiv:0701647 [math.CO], 2007-2008.

R. Bisdorff and J.-L. Marichal, Counting non-isomorphic maximal independent sets of the n-cycle graph, JIS 11 (2008), #08.5.7.

D. J. Broadhurst and D. Kreimer, Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops, UTAS-PHYS-96-44; arXiv:hep-th/9609128, 1996.

D. J. Broadhurst and D. Kreimer, Associated multiple zeta values with positive knots via Feynman diagrams up to 9 knots, Phys. Lett B, 393 (1997), 403-412.

M. Waldschmidt, Lectures on Multiple Zeta Values, IMSC 2011.

FORMULA

a(n) = (1/n) * Sum_{d|n} mu(n/d)*Perrin(d), where Perrin(d) = A001608 starting with 0, 2, 3, ... .

a(n) = Sum_{d|n} mu(n/d)*A127687(d) = (1/n) * Sum_{d|n} mu(n/d)*A001608(d). - Jean-Luc Marichal (jean-luc.marichal(AT)uni.lu), Jan 24 2007

For p an odd prime, a(p) = Sum_{i=0..floor((p-3)/6)} (A(i)+B(i)-1)!/(A(i)!*B(i)!), where A(i) = (p-3)/2 - 3*i, and B(i) = 1 + 2*i. - Richard Turk, Sep 08 2015

a(n) ~ A060006^n / n. - Vaclav Kotesovec, Oct 09 2019

MAPLE

A113788 := proc(n::integer)

local resul, d;

resul :=0;

for d from 1 to n do

if n mod d = 0 then

resul := resul +numtheory[mobius](n/d)*A001608(d);

fi;

od:

RETURN(resul/n);

end: # R. J. Mathar, Apr 25 2006

MATHEMATICA

(* p = A001608 *) p[n_] := p[n] = p[n-2] + p[n-3]; p[0] = 3; p[1] = 0; p[2] = 2; a[n_] := (1/n)*Sum[MoebiusMu[n/d]*p[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 56}] (* Jean-François Alcover, Jul 16 2012, from first formula *)

PROG

(Sage)

z = PowerSeriesRing(ZZ, 'z').gen().O(30)

r = (1 - (z**2 + z**3))

F = -z*r.derivative()/r

[sum(moebius(n//d)*F[d] for d in divisors(n))//n for n in range(1, 24)] # F. Chapoton, Apr 24 2020

CROSSREFS

Cf. A001608, A127687, A125951.

Sequence in context: A036823 A035575 A036816 * A018243 A127207 A173513

Adjacent sequences: A113785 A113786 A113787 * A113789 A113790 A113791

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Jan 27 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 28 05:31 EST 2022. Contains 358407 sequences. (Running on oeis4.)