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%I #35 Sep 08 2022 08:44:39
%S 1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,0
%N Inverse of 33rd cyclotomic polynomial.
%C Periodic with period length 33. - _Ray Chandler_, Apr 03 2017
%H Vincenzo Librandi, <a href="/A014042/b014042.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, -1, 1, 0, -1, 1, 0, -1, 1, -1, 0, 1, -1, 0, 1, -1, 0, 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^3 - x^4 + x^6 - x^7 + x^9 - x^10 + x^11 - x^13 + x^14 - x^16 + x^17 - x^19 + x^20). - _Ilya Gutkovskiy_, Aug 19 2017
%F a(n) = (18*m^10 - 950*m^9 + 21645*m^8 - 278400*m^7 + 2216844*m^6 - 11256630*m^5 + 36087705*m^4 - 69333700*m^3 + 70537788*m^2 - 27994320*m + 1814400) * (3*w^2 - 7*w + 2) / 3628800 where m = (n mod 11) and w = (floor(n/11) mod 3). - _Luce ETIENNE_, Nov 20 2018
%p with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%t CoefficientList[Series[1/Cyclotomic[33, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 04 2014 *)
%t LinearRecurrence[{1, 0, -1, 1, 0, -1, 1, 0, -1, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1},{1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0},81] (* _Ray Chandler_, Sep 15 2015 *)
%o (PARI) Vec(1/polcyclo(33)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014
%o (Magma) t:=33; u:=3; m:=u*t+3; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/CyclotomicPolynomial(t))); // _Bruno Berselli_, Apr 04 2014
%Y Column k=33 of A291137.
%Y Cf. A010880, A010872.
%K sign,easy
%O 0,1
%A _Simon Plouffe_
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