A014045 - OEIS

%I #20 Aug 21 2017 05:54:54

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

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

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

%N Inverse of 36th cyclotomic polynomial.

%C Periodic with period length 36. - _Ray Chandler_, Apr 03 2017

%H Vincenzo Librandi, <a href="/A014045/b014045.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 1, 0, 0, 0, 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^6 + x^12). - _Ilya Gutkovskiy_, Aug 19 2017

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

%t CoefficientList[Series[1/Cyclotomic[36, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 04 2014 *)

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

%o (PARI) Vec(1/polcyclo(36)+O(x^99)) \\ _Charles R Greathouse IV_, Apr 01 2014

%Y Column k=36 of A291137.

%K sign,easy

%O 0,1

%A _Simon Plouffe_