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A014019
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Inverse of 10th cyclotomic polynomial.
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7
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1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1
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OFFSET
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0,1
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COMMENTS
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The g.f. is the image of the g.f. of Fib(n+1) by the transform A(x) -> (1/(1 + x^2)^2)*A(x/(1+x^2)). The denominator is associated with the knots 4_1 and 5_1 by their Alexander and Jones polynomials respectively. - Paul Barry, Oct 16 2004
For n >= 1, a(n) is the determinant of an n X n Toeplitz matrix M satisfying: M(i,j) = 1 if -1 <= j - i <= 3 and 0 otherwise. - Dmitry Efimov, Jun 23 2015
Period 10: repeat [1,1,0,0,0,-1,-1,0,0,0]. - Wesley Ivan Hurt, Jun 24 2015
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LINKS
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FORMULA
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G.f.: 1/(1 - x + x^2 - x^3 + x^4). - Paul Barry, Oct 16 2004
a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4), n > 4. - Wesley Ivan Hurt, Jun 24 2015
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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[10, x], {x, 0, 100}], x] (* Vincenzo Librandi, Apr 03 2014 *)
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PROG
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(Magma) &cat[[1, 1, 0, 0, 0, -1, -1, 0, 0, 0]: n in [0..15]]; // 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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