A014051 - OEIS

%I #22 Apr 03 2017 12:35:34

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

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

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

%N Inverse of 42nd cyclotomic polynomial.

%C Periodic with period length 42. - _Ray Chandler_, Apr 03 2017

%H Vincenzo Librandi, <a href="/A014051/b014051.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 0, 1, 1, 0, -1, 0, 1, 1, 0, -1, -1).

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

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

%t CoefficientList[Series[1/Cyclotomic[42, x], {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 04 2014 *)

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

%o (PARI) Vec(1/polcyclo(42)+O(x^99)) \\ _Charles R Greathouse IV_, Apr 01 2014

%Y Cf. inverse of  k-th cyclotomic polynomial: A049347 (k=3), A056594 (k=4), A010891 (k=5),  A010892 (k=6),  A014016 - A014045 (k=7-36),  A240328 (k=37),  A014047 - A014049 (k=38-40), A240329 (k=41).

%K sign,easy

%O 0,1

%A _Simon Plouffe_