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%I #50 Dec 14 2023 05:51:07
%S 1,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,0,
%T 1,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,0,
%U 1,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,0,1
%N Inverse of 8th cyclotomic polynomial.
%C Periodic with period length 8. - _Ray Chandler_, Apr 03 2017
%H Vincenzo Librandi, <a href="/A014017/b014017.txt">Table of n, a(n) for n = 0..1000</a>
%H John M. Campbell, <a href="http://arxiv.org/abs/1105.3399">An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences</a>, arXiv preprint arXiv:1105.3399 [math.GM], 2011.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,-1).
%H <a href="/index/Pol#poly_cyclo_inv">Index to sequences related to inverse of cyclotomic polynomials</a>
%F a(4n) = (-1)^n, else a(n) = 0.
%F G.f.: 1/ ( 1+x^4 ). - _R. J. Mathar_, Mar 11 2011
%F a(n) = sin((sin(Pi*(n+1)/2)^2)*Pi*(n+2)/4). - _Mikael Aaltonen_, Jan 02 2015
%F E.g.f.: cos(x/sqrt(2))*cosh(x/sqrt(2)). - _Vaclav Kotesovec_, Feb 15 2015
%p with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%t CoefficientList[Series[1/Cyclotomic[8, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 03 2014 *)
%o (PARI) Vec(1/polcyclo(8)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014
%o (Magma) &cat[[1,0,0,0,-1,0,0,0]: n in [0..20]]; // _Vincenzo Librandi_, Apr 03 2014
%K sign,easy
%O 0,1
%A _Simon Plouffe_
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