A014064 - OEIS

%I #30 Jan 27 2019 09:51:42

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

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

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

%N Coefficients of the reciprocal of the 55th cyclotomic polynomial.

%C Periodic with period length 55. - _Ray Chandler_, Apr 03 2017

%H Vincenzo Librandi, <a href="/A014064/b014064.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_40">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1).

%H <a href="/index/Pol#poly_cyclo_inv">Index to sequences related to inverse of cyclotomic polynomials</a>

%F a(n) = (5*w - 1)*(w - 2)*(w - 3)*(w - 4)*(63*m^4 - 350*m^3 + 630*m^2 - 325*m + 12)*(m - 5)!/(43545600*(m - 11)!), where m = n mod 11 and w = floor(n/11) mod 5. - _Luce ETIENNE_, Nov 21 2018

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

%t CoefficientList[Series[1/Cyclotomic[55, x], {x, 0, 200}], x] (* _Vincenzo Librandi_, Apr 05 2014 *)

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

%o (PARI) Vec(1/polcyclo(55) + O(x^99)) \\ _Michel Marcus_, Jan 25 2019

%Y Cf. similar sequences listed in A240328.

%Y Cf. A010880, A010874.

%K sign,easy

%O 0,1

%A _Simon Plouffe_

%E Name edited by _Wolfdieter Lang_, Jan 25 2019