cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A014020 Inverse of 11th cyclotomic polynomial.

This page as a plain text file.
%I A014020 #32 Sep 08 2022 08:44:39
%S A014020 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 A014020 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 A014020 1,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0
%N A014020 Inverse of 11th cyclotomic polynomial.
%C A014020 Periodic with period 11. - _Ray Chandler_, Apr 03 2017
%H A014020 Vincenzo Librandi, <a href="/A014020/b014020.txt">Table of n, a(n) for n = 0..1000</a>
%H A014020 <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 A014020 <a href="/index/Pol#poly_cyclo_inv">Index to sequences related to inverse of cyclotomic polynomials</a>
%F A014020 G.f.: 1/(1 + x + x^2 + x^3 + ... + x^10). - _R. J. Mathar_, Aug 11 2012
%F A014020 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 A014020 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%t A014020 CoefficientList[Series[1/Cyclotomic[11, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 03 2014 *)
%t A014020 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 A014020 (PARI) Vec(1/polcyclo(11)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014
%o A014020 (Magma) &cat[[1,-1,0,0,0,0,0,0,0,0,0]: n in [0..15]]; // _Vincenzo Librandi_, Apr 03 2014
%Y A014020 Cf. A010880.
%K A014020 sign,easy
%O A014020 0,1
%A A014020 _Simon Plouffe_