%I #34 Nov 05 2025 15:21:47

%S 1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,

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

%N Inverse of 34th cyclotomic polynomial.

%C Periodic with period length 34. - _Ray Chandler_, Apr 03 2017

%H Vincenzo Librandi, <a href="/A014043/b014043.txt">Table of n, a(n) for n = 0..1000</a>

%H S. Kitaev, J. Remmel and M. Tiefenbruck, <a href="https://arxiv.org/abs/1201.6243">Marked mesh patterns in 132-avoiding permutations I</a>, arXiv preprint arXiv:1201.6243 [math.CO], 2012. - _N. J. A. Sloane_, May 09 2012

%H <a href="/index/Rec#order_16">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).

%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^4 - x^5 + ... + x^16). - _Ilya Gutkovskiy_, Aug 19 2017

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

%t CoefficientList[Series[1/Cyclotomic[34, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},81] (* _Ray Chandler_, Sep 15 2015 *)

%o (PARI) Vec(1/polcyclo(34)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014

%o (Magma) t:=34; u:=3; m:=u*t+2; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/CyclotomicPolynomial(t))); // _Bruno Berselli_, Apr 04 2014

%Y Column k=34 of A291137.

%K sign,easy

%O 0,1

%A _Simon Plouffe_