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A014040
Inverse of 31st cyclotomic polynomial.
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, 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, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,1
COMMENTS
Periodic with period length 31. - Ray Chandler, Apr 03 2017
LINKS
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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1).
FORMULA
G.f.: 1/(1 + x + x^2 + x^3 + ... + x^30). - Ilya Gutkovskiy, Aug 19 2017
MAPLE
with(numtheory, cyclotomic); c := n->series(1/cyclotomic(n, x), x, 80);
MATHEMATICA
CoefficientList[Series[1/Cyclotomic[31, 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, -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}, 81] (* Ray Chandler, Sep 15 2015 *)
PROG
(PARI) Vec(1/polcyclo(31)+O(x^99)) \\ Charles R Greathouse IV, Mar 24 2014
(Magma) &cat[[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]: n in [0..4]]; // Vincenzo Librandi, Apr 04 2014
CROSSREFS
Column k=31 of A291137.
Sequence in context: A240329 A240328 A240357 * A014071 A014038 A014067
KEYWORD
sign
AUTHOR
STATUS
approved