%I #32 Sep 08 2022 08:44:39
%S 1,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,
%T 1,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,
%U 1,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0
%N Inverse of 11th cyclotomic polynomial.
%C Periodic with period 11. - _Ray Chandler_, Apr 03 2017
%H Vincenzo Librandi, <a href="/A014020/b014020.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (-1, -1, -1, -1, -1, -1, -1, -1, -1, -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 + x^2 + x^3 + ... + x^10). - _R. J. Mathar_, Aug 11 2012
%F a(n) = (11*m^10 - 595*m^9 + 13980*m^8 - 186990*m^7 + 1566663*m^6 - 8513715*m^5 + 29974570*m^4 - 65946860*m^3 + 82751976*m^2 - 46916640*m + 3628800)/3628800, where m = n mod 11. - _Luce ETIENNE_, Sep 20 2018
%p with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%t CoefficientList[Series[1/Cyclotomic[11, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 03 2014 *)
%t LinearRecurrence[{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1},{1, -1, 0, 0, 0, 0, 0, 0, 0, 0},81] (* _Ray Chandler_, Sep 15 2015 *)
%o (PARI) Vec(1/polcyclo(11)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014
%o (Magma) &cat[[1,-1,0,0,0,0,0,0,0,0,0]: n in [0..15]]; // _Vincenzo Librandi_, Apr 03 2014
%Y Cf. A010880.
%K sign,easy
%O 0,1
%A _Simon Plouffe_