A014017 Inverse of 8th cyclotomic polynomial.

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

Offset: 0

Author

Simon Plouffe

Keywords

• sign
• easy

Comments

Periodic with period length 8. - Ray Chandler, Apr 03 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• John M. Campbell, An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences, arXiv preprint arXiv:1105.3399 [math.GM], 2011.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,-1).
• Index to sequences related to inverse of cyclotomic polynomials

Programs

Magma

&cat[[1,0,0,0,-1,0,0,0]: n in [0..20]]; // Vincenzo Librandi, Apr 03 2014

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[8, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)

PARI

Vec(1/polcyclo(8)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014

Formula

a(4n) = (-1)^n, else a(n) = 0.

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

a(n) = sin((sin(Pi*(n+1)/2)^2)*Pi*(n+2)/4). - Mikael Aaltonen, Jan 02 2015

E.g.f.: cos(x/sqrt(2))*cosh(x/sqrt(2)). - Vaclav Kotesovec, Feb 15 2015