A014027 - OEIS

%I #34 Dec 14 2023 05:51:42

%S 1,0,0,1,0,0,0,0,0,-1,0,0,-1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,-1,0,0,-1,0,

%T 0,0,0,0,1,0,0,1,0,0,0,0,0,-1,0,0,-1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,-1,0,

%U 0,-1,0,0,0,0,0,1,0,0,1,0,0,0,0,0

%N Inverse of 18th cyclotomic polynomial.

%C Periodic with period length 18. - _Ray Chandler_, Apr 03 2017

%H Vincenzo Librandi, <a href="/A014027/b014027.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 1, 0, 0, -1).

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

%F G.f.: 1 / ( 1-x^3+x^6 ). - _R. J. Mathar_, Mar 11 2011

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

%t CoefficientList[Series[1/Cyclotomic[18, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 03 2014 *)

%t LinearRecurrence[{0, 0, 1, 0, 0, -1},{1, 0, 0, 1, 0, 0},81] (* _Ray Chandler_, Sep 15 2015 *)

%o (PARI) Vec(1/polcyclo(18)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014

%o (Magma) &cat[[1,0,0,1,0,0,0,0,0,-1,0,0,-1,0,0,0,0,0]: n in [0..8]]; // _Vincenzo Librandi_, Apr 03 2014

%K sign,easy

%O 0,1

%A _Simon Plouffe_