|
%I #24 Sep 08 2022 08:44:39
%S 1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T 0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Inverse of 27th cyclotomic polynomial.
%C Periodic with period length 27. - _Ray Chandler_, Apr 03 2017
%H Vincenzo Librandi, <a href="/A014036/b014036.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -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^9 + x^18). - _Ilya Gutkovskiy_, Aug 19 2017
%p with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n, x), x,80); c(27);
%t CoefficientList[Series[1/Cyclotomic[27, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 03 2014 *)
%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1},{1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0},81] (* _Ray Chandler_, Sep 15 2015 *)
%o (PARI) Vec(1/polcyclo(27)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014
%o (Magma) &cat[[1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]: n in [0..5]]; // _Vincenzo Librandi_, Apr 03 2014
%Y Column k=27 of A291137.
%K sign,easy
%O 0,1
%A _Simon Plouffe_
|
