A014064 Coefficients of the reciprocal of the 55th cyclotomic polynomial.

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

Offset: 0

Author

Simon Plouffe

Keywords

• sign
• easy

Comments

Periodic with period length 55. - 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, 0, 0, -1, 1, 0, 0, 0, -1, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1).
• Index to sequences related to inverse of cyclotomic polynomials

Crossrefs

Cf. similar sequences listed in A240328.

Cf. A010880, A010874.

Programs

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[55, x], {x, 0, 200}], x] (* Vincenzo Librandi, Apr 05 2014 *)
LinearRecurrence[{1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1},{1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},81] (* Ray Chandler, Sep 15 2015 *)

PARI

Vec(1/polcyclo(55) + O(x^99)) \\ Michel Marcus, Jan 25 2019

Formula

a(n) = (5*w - 1)*(w - 2)*(w - 3)*(w - 4)*(63*m^4 - 350*m^3 + 630*m^2 - 325*m + 12)*(m - 5)!/(43545600*(m - 11)!), where m = n mod 11 and w = floor(n/11) mod 5. - Luce ETIENNE, Nov 21 2018

Extensions

Name edited by Wolfdieter Lang, Jan 25 2019