A014039 Inverse of 30th cyclotomic polynomial.

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

Offset

0,1

Comments

Periodic with period length 30. - 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, 1, 1, 1, 0, -1, -1).

Index to sequences related to inverse of cyclotomic polynomials

Formula

G.f.: 1/(1 + x - x^3 - x^4 - x^5 + x^7 + x^8). - Ilya Gutkovskiy, Aug 19 2017

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[30, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{-1, 0, 1, 1, 1, 0, -1, -1}, {1, -1, 1, 0, 0, 1, -1, 1}, 81] (* Ray Chandler, Sep 15 2015 *)

Prog

(PARI) Vec(1/polcyclo(30)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[1, -1, 1, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0]: n in [0..4]]; // Vincenzo Librandi, Apr 03 2014

Crossrefs

Column k=30 of A291137.

Sequence in context: A281011 A016416 A014024 * A016410 A230412 A115361

Adjacent sequences: A014036 A014037 A014038 * A014040 A014041 A014042

Keyword

sign

Author

Simon Plouffe

Status

approved