A010891 - OEIS

A010891

Inverse of 5th cyclotomic polynomial.

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

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OFFSET

0,1

COMMENTS

D(n):= a(n+3) appears in the formula 2*exp(2*Pi*I/5) = (A(n+ B(n)*phi) + (C(n) + D(n)*phi)*sqrt(2 + phi)*I, with the golden section phi, I = sqrt(-1) and A(n) = A164116(n+5), B(n) = A080891(n) and C(n) = A156174(n+4) for n >= 0. See one of the comments on A164116. - Wolfdieter Lang, Feb 26 2014

Periodic with period length 5. - 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 (-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 ). - R. J. Mathar, Mar 11 2011

MAPLE

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

MATHEMATICA

CoefficientList[Series[1/Cyclotomic[5, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)

PROG