A015582 Inverse of 1573rd cyclotomic polynomial.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Author

Simon Plouffe

Keywords

• sign

Comments

Periodic with period length 1573. - Ray Chandler, Apr 07 2017

Links

• Ray Chandler, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, order 1320.
• Index to sequences related to inverse of cyclotomic polynomials

Crossrefs

Different from A014856 and A100910.

Programs

Maple

with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n, x), x,80); c(1573);

Mathematica

CoefficientList[Series[1/Cyclotomic[1573, x], {x, 0, 100}], x][[;; 81]] (* Jean-François Alcover, Jul 05 2011 *)

Formula

cyclotomic(1573,x) is a polynomial of 120th order in the variable x^11, so it is c = 1 - x^11 - x^132 + x^264 + ... + x^1320, or with y = x^11 we can write c = 1 - y + y^11 - y^12 + y^13 - y^14 ... + y^120. - R. J. Mathar, Oct 20 2008

Extensions

Incorrect formula deleted by N. J. A. Sloane, Oct 20 2008