A014262 Inverse of 253rd cyclotomic polynomial.

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

Offset: 0

Author

Simon Plouffe

Keywords

• sign
• easy

Comments

Periodic with period length 253. - Ray Chandler, Apr 03 2017

In general the expansion of 1/Phi(N) is N-periodic, but also satisfies a linear recurrence of lower order given by degree(Phi(N)) = phi(N) = A000010(N) < N. The signature is given by the coefficients of (1-Phi(N)). - M. F. Hasler, Feb 18 2018

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, order 220.
• Index to sequences related to inverse of cyclotomic polynomials

Crossrefs

Cf. similar sequences listed in A240328, A240467.

Programs

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[253, x], {x, 0, 200}], x] (* Vincenzo Librandi, Apr 07 2014 *)

PARI

Vec(1/polcyclo(253)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014