A014034 Inverse of 25th cyclotomic polynomial.

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

Offset

0,1

Comments

Periodic with period length 25. - 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, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1).

Index to sequences related to inverse of cyclotomic polynomials

Formula

G.f.: 1/(1 + x^5 + x^10 + x^15 + x^20). - Ilya Gutkovskiy, Aug 18 2017

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[25, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 81] (* Ray Chandler, Sep 15 2015 *)

Prog

(PARI) Vec(1/polcyclo(25)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]: n in [0..5]]; // Vincenzo Librandi, Apr 03 2014

Crossrefs

Sequence in context: A080111 A204545 A185116 * A014059 A015934 A016284

Adjacent sequences: A014031 A014032 A014033 * A014035 A014036 A014037

Keyword

sign,easy

Author

Simon Plouffe

Status

approved