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

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

(PARI) Vec(1/polcyclo(5)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[1, -1, 0, 0, 0]: n in [0..20]]; // Vincenzo Librandi, Apr 03 2014

Crossrefs

Sequence in context: A015439 A016379 A016339 * A014019 A016349 A016392

Adjacent sequences: A010888 A010889 A010890 * A010892 A010893 A010894

Keyword

sign,easy

Author

Simon Plouffe

Status

approved