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Inverse of 30th cyclotomic polynomial.
2

%I #21 Sep 08 2022 08:44:39

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

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

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

%N Inverse of 30th cyclotomic polynomial.

%C Periodic with period length 30. - _Ray Chandler_, Apr 03 2017

%H Vincenzo Librandi, <a href="/A014039/b014039.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 0, 1, 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^5 + x^7 + x^8). - _Ilya Gutkovskiy_, Aug 19 2017

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

%t CoefficientList[Series[1/Cyclotomic[30, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 03 2014 *)

%t LinearRecurrence[{-1, 0, 1, 1, 1, 0, -1, -1},{1, -1, 1, 0, 0, 1, -1, 1},81] (* _Ray Chandler_, Sep 15 2015 *)

%o (PARI) Vec(1/polcyclo(30)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014

%o (Magma) &cat[[1, -1, 1, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0]: n in [0..4]]; // _Vincenzo Librandi_, Apr 03 2014

%Y Column k=30 of A291137.

%K sign

%O 0,1

%A _Simon Plouffe_