A014515 - OEIS

%I #19 Feb 13 2022 16:56:24

%S 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,

%T -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,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Inverse of 506th cyclotomic polynomial.

%C Periodic with period length 506. - _Ray Chandler_, Apr 04 2017

%C 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

%H Ray Chandler, <a href="/A014515/b014515.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_220">Index entries for linear recurrences with constant coefficients</a>, order 220.

%H <a href="/index/Pol#poly_cyclo_inv">Index to sequences related to inverse of cyclotomic polynomials</a>

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

%t CoefficientList[Series[1/Cyclotomic[506,x],{x,0,120}],x,120] (* _Harvey P. Dale_, Feb 13 2022 *)

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

%K sign

%O 0,1

%A _Simon Plouffe_