A014033 Inverse of 24th cyclotomic polynomial.

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

Offset: 0

Author

Simon Plouffe

Keywords

• sign
• easy

Comments

Periodic with period length 24. - 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 (0, 0, 0, 1, 0, 0, 0, -1).
• Index to sequences related to inverse of cyclotomic polynomials

Programs

Magma

&cat[[1,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,-1,0,0,0, 0,0,0,0]: n in [0..5]]; // Vincenzo Librandi, Apr 03 2014

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[24, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{0, 0, 0, 1, 0, 0, 0, -1},{1, 0, 0, 0, 1, 0, 0, 0},81] (* Ray Chandler, Sep 15 2015 *)

PARI

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

Formula

|a(n)| = A000388(n+10)(mod 2). - John M. Campbell, Jul 13 2016

G.f.: 1/(1 - x^4 + x^8). - Ilya Gutkovskiy, Aug 18 2017