A014025 Expansion of the inverse of the 16th cyclotomic polynomial.

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

Offset

0,1

Comments

Period 16: repeat [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0].

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, 0, 0, 0, -1).

Index to sequences related to inverse of cyclotomic polynomials

Formula

G.f.: 1/(1 + x^8). - Klaus Brockhaus, May 17 2011

a(n) = -a(n-8).

abs(a(n)) = floor(1/2*cos(n*Pi/4)+1/2). - Gary Detlefs, May 16 2011

a(n)=(floor((n+8)/8)-floor((n+7)/8))*(-1)^floor(n/8). |a(n)| is the characteristic function of numbers that are multiples of 8. |a(n)|=floor(n/8)-floor((n-1)/8). - Boris Putievskiy, May 08 2013

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[16, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, 0, 0, 0}, 99] (* Ray Chandler, Sep 15 2015 *)

Prog

(PARI) Vec(1/polcyclo(16)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0]: n in [0..8]]; // Vincenzo Librandi, Apr 03 2014

Crossrefs

Sequence in context: A369034 A015241 A253513 * A279760 A287457 A358777

Adjacent sequences: A014022 A014023 A014024 * A014026 A014027 A014028

Keyword

sign,easy

Author

Simon Plouffe

Status

approved