A014018 Inverse of 9th cyclotomic polynomial.

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

Offset

0,1

Comments

Periodic with period length 9. - 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, 0, -1, 0, 0, -1).

Index to sequences related to inverse of cyclotomic polynomials

Formula

G.f.: 1/(1 + x^3 + x^6). - Ilya Gutkovskiy, Aug 18 2017

a(n) = (19*m^8 - 628*m^7 + 8526*m^6 - 61152*m^5 + 247611*m^4 - 558012*m^3 + 637604*m^2 - 287408*m + 13440)/13440, where m = n mod 9. - Luce ETIENNE, Oct 18 2018

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[9, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{0, 0, -1, 0, 0, -1}, {1, 0, 0, -1, 0, 0}, 81] (* Ray Chandler, Sep 15 2015 *)

Prog

(PARI) Vec(1/polcyclo(9)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[1, 0, 0, -1, 0, 0, 0, 0, 0]: n in [0..15]]; // Vincenzo Librandi, Apr 03 2014

Crossrefs

Cf. A010878.

Sequence in context: A014828 A015647 A015998 * A014027 A015296 A015890

Adjacent sequences: A014015 A014016 A014017 * A014019 A014020 A014021

Keyword

sign,easy

Author

Simon Plouffe

Status

approved