cp's OEIS Frontend

A014016 Expansion of inverse of 7th cyclotomic polynomial; period 7: repeat [1, -1, 0, 0, 0, 0, 0].

%I A014016 #44 Dec 14 2023 05:51:11
%S A014016 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,
%T A014016 0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,
%U A014016 -1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0
%N A014016 Expansion of inverse of 7th cyclotomic polynomial; period 7: repeat [1, -1, 0, 0, 0, 0, 0].
%H A014016 Vincenzo Librandi, <a href="/A014016/b014016.txt">Table of n, a(n) for n = 0..1000</a>
%H A014016 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,-1,-1,-1).
%H A014016 <a href="/index/Pol#poly_cyclo_inv">Index to sequences related to inverse of cyclotomic polynomials</a>
%F A014016 G.f.: 1 / ( 1+x+x^2+x^3+x^4+x^5+x^6 ). - _R. J. Mathar_, Mar 11 2011
%F A014016 From _Wesley Ivan Hurt_, Jul 18 2016: (Start)
%F A014016 a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) for n>5.
%F A014016 a(n) = 1 + floor(n/7) + floor((5+n)/7) - 2*floor((6+n)/7). (End)
%p A014016 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%t A014016 CoefficientList[Series[1/Cyclotomic[7, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 03 2014 *)
%t A014016 PadRight[{},120,{1,-1,0,0,0,0,0}] (* or *) LinearRecurrence[{-1,-1,-1,-1,-1,-1},{1,-1,0,0,0,0},120] (* _Harvey P. Dale_, Jan 11 2015 *)
%o A014016 (PARI) Vec(1/polcyclo(7)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 24 2014
%o A014016 (Magma) &cat[[1,-1,0,0,0,0,0]: n in [0..20]]; // _Vincenzo Librandi_, Apr 03 2014
%K A014016 sign,easy
%O A014016 0,1
%A A014016 _Simon Plouffe_