A014020 Inverse of 11th 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 11. - 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]: 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[11, 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(11)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014

Formula

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

a(n) = (11*m^10 - 595*m^9 + 13980*m^8 - 186990*m^7 + 1566663*m^6 - 8513715*m^5 + 29974570*m^4 - 65946860*m^3 + 82751976*m^2 - 46916640*m + 3628800)/3628800, where m = n mod 11. - Luce ETIENNE, Sep 20 2018