A014515 Inverse of 506th cyclotomic polynomial.

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

Offset

0,1

Comments

Periodic with period length 506. - Ray Chandler, Apr 04 2017

In general the expansion of 1/Phi(N) is N-periodic, but also satisfies a linear recurrence of lower order given by degree(Phi(N)) = phi(N) = A000010(N) < N. The signature is given by the coefficients of (1-Phi(N)). - M. F. Hasler, Feb 18 2018

Links

Ray Chandler, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, order 220.

Index to sequences related to inverse of cyclotomic polynomials

Maple

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

Mathematica

CoefficientList[Series[1/Cyclotomic[506, x], {x, 0, 120}], x, 120] (* Harvey P. Dale, Feb 13 2022 *)

Crossrefs

Cf. sequences listed in cross-references of A240328 (1/Phi(N), N = 3 .. 75) and A240467 (N = 76 .. 253).

Sequence in context: A014328 A014647 A014262 * A014218 A014427 A014196

Adjacent sequences: A014512 A014513 A014514 * A014516 A014517 A014518

Keyword

sign

Author

Simon Plouffe

Status

approved