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.

A014018 Inverse of 9th cyclotomic polynomial.

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%I A014018 #30 Sep 08 2022 08:44:39
%S A014018 1,0,0,-1,0,0,0,0,0,1,0,0,-1,0,0,0,0,0,1,0,0,-1,0,0,0,0,0,1,0,0,-1,0,
%T A014018 0,0,0,0,1,0,0,-1,0,0,0,0,0,1,0,0,-1,0,0,0,0,0,1,0,0,-1,0,0,0,0,0,1,0,
%U A014018 0,-1,0,0,0,0,0,1,0,0,-1,0,0,0,0,0
%N A014018 Inverse of 9th cyclotomic polynomial.
%C A014018 Periodic with period length 9. - _Ray Chandler_, Apr 03 2017
%H A014018 Vincenzo Librandi, <a href="/A014018/b014018.txt">Table of n, a(n) for n = 0..1000</a>
%H A014018 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, -1, 0, 0, -1).
%H A014018 <a href="/index/Pol#poly_cyclo_inv">Index to sequences related to inverse of cyclotomic polynomials</a>
%F A014018 G.f.: 1/(1 + x^3 + x^6). - _Ilya Gutkovskiy_, Aug 18 2017
%F A014018 a(n) = (19*m^8 - 628*m^7 + 8526*m^6 - 61152*m^5 + 247611*m^4 - 558012*m^3 + 637604*m^2 - 287408*m + 13440)/13440, where m = n mod 9. - _Luce ETIENNE_, Oct 18 2018
%p A014018 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%t A014018 CoefficientList[Series[1/Cyclotomic[9, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 03 2014 *)
%t A014018 LinearRecurrence[{0, 0, -1, 0, 0, -1},{1, 0, 0, -1, 0, 0},81] (* _Ray Chandler_, Sep 15 2015 *)
%o A014018 (PARI) Vec(1/polcyclo(9)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014
%o A014018 (Magma) &cat[[1,0,0,-1,0,0,0,0,0]: n in [0..15]]; // _Vincenzo Librandi_, Apr 03 2014
%Y A014018 Cf. A010878.
%K A014018 sign,easy
%O A014018 0,1
%A A014018 _Simon Plouffe_