A014027 Inverse of 18th cyclotomic polynomial.

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

Offset

0,1

Comments

Periodic with period length 18. - 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, 1, 0, 0, -1).

Index to sequences related to inverse of cyclotomic polynomials

Formula

a(n) = (1/18)*(-(n mod 18)-((n+5) mod 18)+((n+6) mod 18)-((n+8) mod 18)+((n+9) mod 18)+((n+14) mod 18)-((n+15) mod 18)+((n+17) mod 18)). - Paolo P. Lava, Mar 10 2011

G.f.: 1 / ( 1-x^3+x^6 ). - R. J. Mathar, Mar 11 2011

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[18, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{0, 0, 1, 0, 0, -1}, {1, 0, 0, 1, 0, 0}, 81] (* Ray Chandler, Sep 15 2015 *)

Prog

(PARI) Vec(1/polcyclo(18)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0]: n in [0..8]]; // Vincenzo Librandi, Apr 03 2014

Crossrefs

Sequence in context: A015647 A015998 A014018 * A015296 A015890 A011648

Adjacent sequences: A014024 A014025 A014026 * A014028 A014029 A014030

Keyword

sign,easy

Author

Simon Plouffe

Status

approved