A014021 Inverse of 12th cyclotomic polynomial.

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

Offset: 0

Author

Simon Plouffe

Keywords

• sign
• easy

Comments

Periodic with period length 12. - 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, 1, 0, -1).
• Index to sequences related to inverse of cyclotomic polynomials

Programs

Magma

&cat[[1,0,1,0,0,0,-1,0,-1,0,0,0]: 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[12, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{0,1,0,-1},{1,0,1,0},100] (* or *) PadRight[{},100,{1,0,1,0,0,0,-1,0,-1,0,0,0}] (* Harvey P. Dale, Oct 12 2017 *)

PARI

Vec(1/polcyclo(12)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014

Formula

G.f.: 1 / ( 1-x^2+x^4 ). - R. J. Mathar, Mar 11 2011