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A240329 Inverse of 41st cyclotomic polynomial. 4

%I #22 Sep 08 2022 08:46:07

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

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

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

%N Inverse of 41st cyclotomic polynomial.

%C Periodic with period length 41. - _Ray Chandler_, Apr 03 2017

%H Vincenzo Librandi, <a href="/A240329/b240329.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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1).

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

%t CoefficientList[Series[1/Cyclotomic[41, x], {x, 0, 100}], x]

%t LinearRecurrence[{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},84] (* _Ray Chandler_, Sep 15 2015 *)

%o (Magma) &cat[[n le 2 select -(-1)^(n) else 0: n in [1..41]]: m in [1..4]];

%o (PARI) Vec(1/polcyclo(41) + O(x^99)) \\ _Jinyuan Wang_, Feb 28 2020

%Y Cf. similar sequences listed in A240328.

%K sign,easy

%O 0

%A _Vincenzo Librandi_, Apr 04 2014

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)