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A014043
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Inverse of 34th cyclotomic polynomial.
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2
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1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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Periodic with period length 34. - Ray Chandler, Apr 03 2017
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
S. Kitaev, J. Remmel and M. Tiefenbruck, Marked mesh patterns in 132-avoiding permutations I, arXiv preprint arXiv:1201.6243 [math.CO], 2012. - N. J. A. Sloane, May 09 2012
Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1).
Index to sequences related to inverse of cyclotomic polynomials
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FORMULA
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G.f.: 1/(1 - x + x^2 - x^3 + x^4 - x^5 + ... + x^16). - Ilya Gutkovskiy, Aug 19 2017
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MAPLE
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with(numtheory, cyclotomic); c := n->series(1/cyclotomic(n, x), x, 80);
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MATHEMATICA
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CoefficientList[Series[1/Cyclotomic[34, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 04 2014 *)
LinearRecurrence[{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}, 81] (* Ray Chandler, Sep 15 2015 *)
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PROG
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(PARI) Vec(1/polcyclo(34)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(MAGMA) t:=34; u:=3; m:=u*t+2; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/CyclotomicPolynomial(t))); // Bruno Berselli, Apr 04 2014
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CROSSREFS
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Column k=34 of A291137.
Sequence in context: A016411 A205987 A014026 * A016422 A016399 A016383
Adjacent sequences: A014040 A014041 A014042 * A014044 A014045 A014046
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KEYWORD
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sign,easy
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AUTHOR
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Simon Plouffe
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STATUS
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approved
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