A014043 Inverse of 34th cyclotomic polynomial.

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,1

Comments

Periodic with period length 34. - Ray Chandler, Apr 03 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

S. Kitaev, J. Remmel and M. Tiefenbruck, Marked mesh patterns in 132-avoiding permutations I, arXiv preprint arXiv:1201.6243 [math.CO], 2012. - N. J. A. Sloane, May 09 2012

Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1).

Index to sequences related to inverse of cyclotomic polynomials

Formula

G.f.: 1/(1 - x + x^2 - x^3 + x^4 - x^5 + ... + x^16). - Ilya Gutkovskiy, Aug 19 2017

Maple

with(numtheory, cyclotomic); c := n->series(1/cyclotomic(n, x), x, 80);

Mathematica

CoefficientList[Series[1/Cyclotomic[34, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 04 2014 *)
LinearRecurrence[{1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1}, {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 81] (* Ray Chandler, Sep 15 2015 *)

Prog

(PARI) Vec(1/polcyclo(34)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) t:=34; u:=3; m:=u*t+2; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/CyclotomicPolynomial(t))); // Bruno Berselli, Apr 04 2014

Crossrefs

Column k=34 of A291137.

Sequence in context: A016411 A205987 A014026 * A016422 A016399 A016383

Adjacent sequences: A014040 A014041 A014042 * A014044 A014045 A014046

Keyword

sign,easy

Author

Simon Plouffe

Status

approved