A014016 Expansion of inverse of 7th cyclotomic polynomial; period 7: repeat [1, -1, 0, 0, 0, 0, 0].

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

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1,-1,-1).

Index to sequences related to inverse of cyclotomic polynomials

Formula

G.f.: 1 / ( 1+x+x^2+x^3+x^4+x^5+x^6 ). - R. J. Mathar, Mar 11 2011

From Wesley Ivan Hurt, Jul 18 2016: (Start)

a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) for n>5.

a(n) = 1 + floor(n/7) + floor((5+n)/7) - 2*floor((6+n)/7). (End)

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[7, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
PadRight[{}, 120, {1, -1, 0, 0, 0, 0, 0}] (* or *) LinearRecurrence[{-1, -1, -1, -1, -1, -1}, {1, -1, 0, 0, 0, 0}, 120] (* Harvey P. Dale, Jan 11 2015 *)

Prog

(PARI) Vec(1/polcyclo(7)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[1, -1, 0, 0, 0, 0, 0]: n in [0..20]]; // Vincenzo Librandi, Apr 03 2014

Crossrefs

Sequence in context: A016402 A016377 A016425 * A014023 A016428 A016417

Adjacent sequences: A014013 A014014 A014015 * A014017 A014018 A014019

Keyword

sign,easy

Author

Simon Plouffe

Status

approved