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A014025 Expansion of the inverse of the 16th cyclotomic polynomial.

%I A014025 #40 Dec 14 2023 05:46:00
%S A014025 1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,
%T A014025 0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,
%U A014025 0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0
%N A014025 Expansion of the inverse of the 16th cyclotomic polynomial.
%C A014025 Period 16: repeat [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0].
%H A014025 Vincenzo Librandi, <a href="/A014025/b014025.txt">Table of n, a(n) for n = 0..1000</a>
%H A014025 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, -1).
%H A014025 <a href="/index/Pol#poly_cyclo_inv">Index to sequences related to inverse of cyclotomic polynomials</a>
%F A014025 G.f.: 1/(1 + x^8). - _Klaus Brockhaus_, May 17 2011
%F A014025 a(n) = -a(n-8).
%F A014025 abs(a(n)) = floor(1/2*cos(n*Pi/4)+1/2). - _Gary Detlefs_, May 16 2011
%F A014025 a(n)=(floor((n+8)/8)-floor((n+7)/8))*(-1)^floor(n/8). |a(n)| is the characteristic function of numbers that are multiples of 8. |a(n)|=floor(n/8)-floor((n-1)/8). - _Boris Putievskiy_, May 08 2013
%p A014025 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%t A014025 CoefficientList[Series[1/Cyclotomic[16, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 03 2014 *)
%t A014025 LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, -1},{1, 0, 0, 0, 0, 0, 0, 0},99] (* _Ray Chandler_, Sep 15 2015 *)
%o A014025 (PARI) Vec(1/polcyclo(16)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014
%o A014025 (Magma) &cat[[1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0]: n in [0..8]]; // _Vincenzo Librandi_, Apr 03 2014
%K A014025 sign,easy
%O A014025 0,1
%A A014025 _Simon Plouffe_