A014042 Inverse of 33rd cyclotomic polynomial.
1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1, 0, -1, 1, 0, -1, 1, 0, -1, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1).
- Index to sequences related to inverse of cyclotomic polynomials
Programs
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Magma
t:=33; u:=3; m:=u*t+3; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/CyclotomicPolynomial(t))); // Bruno Berselli, Apr 04 2014 -
Maple
with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
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Mathematica
CoefficientList[Series[1/Cyclotomic[33, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 04 2014 *) LinearRecurrence[{1, 0, -1, 1, 0, -1, 1, 0, -1, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1},{1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0},81] (* Ray Chandler, Sep 15 2015 *) -
PARI
Vec(1/polcyclo(33)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
Formula
G.f.: 1/(1 - x + x^3 - x^4 + x^6 - x^7 + x^9 - x^10 + x^11 - x^13 + x^14 - x^16 + x^17 - x^19 + x^20). - Ilya Gutkovskiy, Aug 19 2017
a(n) = (18*m^10 - 950*m^9 + 21645*m^8 - 278400*m^7 + 2216844*m^6 - 11256630*m^5 + 36087705*m^4 - 69333700*m^3 + 70537788*m^2 - 27994320*m + 1814400) * (3*w^2 - 7*w + 2) / 3628800 where m = (n mod 11) and w = (floor(n/11) mod 3). - Luce ETIENNE, Nov 20 2018
Comments