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

Author

Simon Plouffe

Keywords

• sign
• easy

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

Crossrefs

Cf. A010878.

Programs

Magma

&cat[[1,0,0,-1,0,0,0,0,0]: n in [0..15]]; // Vincenzo Librandi, Apr 03 2014

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 *)

PARI

Vec(1/polcyclo(9)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014

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