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A014031 Inverse of 22nd cyclotomic polynomial.

%I A014031 #33 Sep 08 2022 08:44:39
%S A014031 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 A014031 -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,
%U A014031 0,1,1,0,0,0,0,0,0,0,0,0,-1,-1,0,0
%N A014031 Inverse of 22nd cyclotomic polynomial.
%C A014031 Periodic with period length 22. - _Ray Chandler_, Apr 03 2017
%H A014031 Vincenzo Librandi, <a href="/A014031/b014031.txt">Table of n, a(n) for n = 0..1000</a>
%H A014031 <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 A014031 <a href="/index/Pol#poly_cyclo_inv">Index to sequences related to inverse of cyclotomic polynomials</a>
%F A014031 G.f.: 1/(1 - x + x^2 - x^3 + ... - x^9 + x^10). - _R. J. Mathar_, Aug 11 2012
%F A014031 From _Luce ETIENNE_, Nov 04 2018: (Start)
%F A014031 a(n) = a(n-22).
%F A014031 a(n) = (-9*m^10 + 485*m^9 - 11340*m^8 + 150690*m^7 - 1251117*m^6 + 6709605*m^5 - 23140710*m^4 + 49127860*m^3 - 57244824*m^2 + 25659360*m + 3628800)*(-1)^floor(n/11)/3628800 where m = (n mod 11). (End)
%p A014031 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%t A014031 CoefficientList[Series[1/Cyclotomic[22, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 03 2014 *)
%t A014031 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 A014031 (PARI) Vec(1/polcyclo(22)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014
%o A014031 (Magma) &cat[[1,1,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0, 0,0,0]: n in [0..6]]; // _Vincenzo Librandi_, Apr 03 2014
%Y A014031 Cf. A010880.
%K A014031 sign,easy
%O A014031 0,1
%A A014031 _Simon Plouffe_