A014021 Inverse of 12th cyclotomic polynomial.

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

Offset

0,1

Comments

Periodic with period length 12. - 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).

Index to sequences related to inverse of cyclotomic polynomials

Formula

G.f.: 1 / ( 1-x^2+x^4 ). - R. J. Mathar, Mar 11 2011

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[12, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{0, 1, 0, -1}, {1, 0, 1, 0}, 100] (* or *) PadRight[{}, 100, {1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0}] (* Harvey P. Dale, Oct 12 2017 *)

Prog

(PARI) Vec(1/polcyclo(12)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0]: n in [0..15]]; // Vincenzo Librandi, Apr 03 2014

Crossrefs

Sequence in context: A015101 A145649 A016340 * A015725 A016331 A285142

Adjacent sequences: A014018 A014019 A014020 * A014022 A014023 A014024

Keyword

sign,easy

Author

Simon Plouffe

Status

approved