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

0,1

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

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

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 *)

Prog

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

Crossrefs

Cf. similar sequences listed in A240328.

Cf. A010880, A010874.

Sequence in context: A014179 A014074 A014139 * A014119 A084052 A352677

Adjacent sequences: A014061 A014062 A014063 * A014065 A014066 A014067

Keyword

sign,easy

Author

Simon Plouffe

Extensions

Name edited by Wolfdieter Lang, Jan 25 2019

Status

approved