A014029 Inverse of 20th cyclotomic polynomial.

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

Offset

0,1

Comments

Periodic with period length 20. - 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).

Index to sequences related to inverse of cyclotomic polynomials

Formula

G.f.: 1/(1 - x^2 + x^4 - x^6 + x^8). - Ilya Gutkovskiy, Aug 18 2017

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[20, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{0, 1, 0, -1, 0, 1, 0, -1}, {1, 0, 1, 0, 0, 0, 0, 0}, 81] (* Ray Chandler, Sep 15 2015 *)

Prog

(PARI) Vec(1/polcyclo(20)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0]: n in [0..6]]; // Vincenzo Librandi, Apr 03 2014

Crossrefs

Sequence in context: A089805 A080116 A016359 * A016396 A016386 A016368

Adjacent sequences: A014026 A014027 A014028 * A014030 A014031 A014032

Keyword

sign

Author

Simon Plouffe

Status

approved