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A014031
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Inverse of 22nd cyclotomic polynomial.
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1
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1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0
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OFFSET
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0,1
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COMMENTS
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, -1, 1, -1, 1, -1, 1, -1).
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FORMULA
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G.f.: 1/(1 - x + x^2 - x^3 + ... - x^9 + x^10). - R. J. Mathar, Aug 11 2012
a(n) = a(n-22).
a(n) = (-9*m^10 + 485*m^9 - 11340*m^8 + 150690*m^7 - 1251117*m^6 + 6709605*m^5 - 23140710*m^4 + 49127860*m^3 - 57244824*m^2 + 25659360*m + 3628800)*(-1)^floor(n/11)/3628800 where m = (n mod 11). (End)
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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[22, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
LinearRecurrence[{1, -1, 1, -1, 1, -1, 1, -1, 1, -1}, {1, 1, 0, 0, 0, 0, 0, 0, 0, 0}, 81] (* Ray Chandler, Sep 15 2015 *)
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PROG
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(Magma) &cat[[1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0]: n in [0..6]]; // Vincenzo Librandi, Apr 03 2014
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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