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

Author

Simon Plouffe

Keywords

• sign
• easy

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

Programs

Magma

&cat[[1,-1,0,0,0,0,0]: n in [0..20]]; // Vincenzo Librandi, Apr 03 2014

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 *)

PARI

Vec(1/polcyclo(7)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014

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)