A014037 Inverse of 28th cyclotomic polynomial.

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

Offset

0,1

Comments

Periodic with period length 28. - 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 (0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1).

Index to sequences related to inverse of cyclotomic polynomials

Formula

G.f.: 1/(1 - x^2 + x^4 - x^6 + x^8 - x^10 + x^12). - Ilya Gutkovskiy, Aug 19 2017

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[28, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1}, {1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 81] (* Ray Chandler, Sep 15 2015 *)

Prog

(PARI) Vec(1/polcyclo(28)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]: n in [0..5]]; // Vincenzo Librandi, Apr 03 2014

Crossrefs

Column k=28 of A291137.

Sequence in context: A186719 A353680 A353637 * A016419 A016391 A016378

Adjacent sequences: A014034 A014035 A014036 * A014038 A014039 A014040

Keyword

sign

Author

Simon Plouffe

Status

approved