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A014016 Expansion of inverse of 7th cyclotomic polynomial; period 7: repeat [1, -1, 0, 0, 0, 0, 0]. 6
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 (list; graph; refs; listen; history; text; internal format)
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

a(n) = (1/7)*(-(n mod 7)-((n+5) mod 7)+2*((n+6) mod 7)). - Paolo P. Lava, Mar 10 2011

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

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Last modified October 15 03:04 EDT 2019. Contains 328025 sequences. (Running on oeis4.)