%I #18 Sep 08 2022 08:46:07
%S 1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1
%N Inverse of 43rd cyclotomic polynomial.
%C Periodic with period length 43. - _Ray Chandler_, Apr 03 2017
%H Vincenzo Librandi, <a href="/A240330/b240330.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_42">Index entries for linear recurrences with constant coefficients</a>, signature (-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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>
%t CoefficientList[Series[1/Cyclotomic[43, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 04 2014 *)
%t LinearRecurrence[{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},{1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},88] (* _Ray Chandler_, Sep 15 2015 *)
%o (Magma) &cat[[n le 2 select -(-1)^(n) else 0: n in [1..43]]: m in [1..4]];
%o (Magma) t:=43; u:=3; m:=u*t+2; R<x>:=PowerSeriesRing(Integers(),m); Coefficients(R!(1/CyclotomicPolynomial(t))); // _Bruno Berselli_, Apr 04 2014
%Y Cf. similar sequences listed in A240328.
%K sign,easy
%O 0
%A _Vincenzo Librandi_, Apr 04 2014
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