A014031 - OEIS

%I #33 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,

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

%N Inverse of 22nd cyclotomic polynomial.

%C Periodic with period length 22. - _Ray Chandler_, Apr 03 2017

%H Vincenzo Librandi, <a href="/A014031/b014031.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^9 + x^10). - _R. J. Mathar_, Aug 11 2012

%F From _Luce ETIENNE_, Nov 04 2018: (Start)

%F a(n) = a(n-22).

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

%t CoefficientList[Series[1/Cyclotomic[22, 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(22)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014

%o (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 Cf. A010880.

%K sign,easy

%O 0,1

%A _Simon Plouffe_