A014030 Inverse of 21st cyclotomic polynomial.

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

Offset

0,1

Comments

Periodic with period length 21. - 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, 0, -1, 0, 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^6 - x^8 + x^9 - x^11 + x^12). - Ilya Gutkovskiy, Aug 18 2017

Maple

with(numtheory, cyclotomic); c := n->series(1/cyclotomic(n, x), x, 120); seq(coeff(c(21), x, n), n=0..100);

Mathematica

CoefficientList[Series[1/Cyclotomic[21, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{1, 0, -1, 1, 0, -1, 0, 1, -1, 0, 1, -1}, {1, 1, 1, 0, 0, 0, 0, -1, -1, -1, 0, 0}, 81] (* Ray Chandler, Sep 15 2015 *)

Prog

(PARI) Vec(1/polcyclo(21)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[1, 1, 1, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]: n in [0..6]]; // Vincenzo Librandi, Apr 03 2014

Crossrefs

Sequence in context: A266300 A266605 A016421 * A014051 A016400 A157022

Adjacent sequences: A014027 A014028 A014029 * A014031 A014032 A014033

Keyword

sign,easy

Author

Simon Plouffe

Status

approved