A014031 Inverse of 22nd cyclotomic polynomial.

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

Offset: 0

Author

Simon Plouffe

Keywords

• sign
• easy

Comments

Periodic with period length 22. - 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, -1, 1, -1, 1, -1, 1, -1, 1, -1).
• Index to sequences related to inverse of cyclotomic polynomials

Crossrefs

Cf. A010880.

Programs

Magma

&cat[[1,1,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0, 0,0,0]: n in [0..6]]; // Vincenzo Librandi, Apr 03 2014

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[22, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{1, -1, 1, -1, 1, -1, 1, -1, 1, -1},{1, 1, 0, 0, 0, 0, 0, 0, 0, 0},81] (* Ray Chandler, Sep 15 2015 *)

PARI

Vec(1/polcyclo(22)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014

Formula

G.f.: 1/(1 - x + x^2 - x^3 + ... - x^9 + x^10). - R. J. Mathar, Aug 11 2012

From Luce ETIENNE, Nov 04 2018: (Start)

a(n) = a(n-22).

a(n) = (-9*m^10 + 485*m^9 - 11340*m^8 + 150690*m^7 - 1251117*m^6 + 6709605*m^5 - 23140710*m^4 + 49127860*m^3 - 57244824*m^2 + 25659360*m + 3628800)*(-1)^floor(n/11)/3628800 where m = (n mod 11). (End)