A014044 Inverse of 35th cyclotomic polynomial.

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

Offset

0,1

Comments

Periodic with period length 35. - Ray Chandler, Apr 03 2017

Links

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

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, -1, 0, 1, -1, 1, -1, 0, 0, 0, 1, -1).

Index to sequences related to inverse of cyclotomic polynomials

Formula

G.f.: 1/(1 - x + x^5 - x^6 + x^7 - x^8 + x^10 - x^11 + x^12 - x^13 + x^14 - x^16 + x^17 - x^18 + x^19 - x^23 + x^24). - Ilya Gutkovskiy, Aug 19 2017

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[35, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 04 2014 *)
LinearRecurrence[{1, 0, 0, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, -1, 0, 1, -1, 1, -1, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 81] (* Ray Chandler, Sep 15 2015 *)

Prog

(PARI) Vec(1/polcyclo(35)+O(x^99)) \\ Charles R Greathouse IV, Apr 01 2014

Crossrefs

Column k=35 of A291137.

Sequence in context: A355938 A268240 A104037 * A014079 A071032 A071034

Adjacent sequences: A014041 A014042 A014043 * A014045 A014046 A014047

Keyword

sign,easy

Author

Simon Plouffe

Status

approved