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A231146 Array of coefficients of numerator polynomials of the rational function p(n, x - 1/x), where p(n,x) is the n-th cyclotomic polynomial. 1
1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 0, -1, 0, 1, 1, -1, -3, 2, 5, -2, -3, 1, 1, 1, 1, -1, -1, 1, 1, -1, -5, 4, 12, -8, -15, 8, 12, -4, -5, 1, 1, 1, 0, -4, 0, 7, 0, -4, 0, 1, 1, 0, -6, -1, 15, 3, -19, -3, 15, 1, -6, 0, 1, 1, 1, -3, -2, 5, 2, -3, -1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,20
COMMENTS
If r is a zero of p(n,x) then (1/2)(r +- sqrt(r^2 + 4) are zeros of q(n,x).
LINKS
EXAMPLE
First 6 rows:
1
-1 .. -1 ... 1
-1 ... 1 ... 1
1 ... -1 .. -1 ... 1 ... 1
1 .... 0 .. -1 ... 0 ... 1
1 ... -1 .. -3 ... 2 ... 5 ... -2 ... -3 ... 1 ... 1
First 4 polynomials: 1, -1 - x + x^2, -1 + x + x^2, 1 - x - x^2 + x^3 + x^4.
MATHEMATICA
z = 60; p[n_, x_] := p[x] = Cyclotomic[n, x]; Table[p[n, x], {n, 0, z/4}]; f1[n_, x_] := f1[n, x] = Numerator[Factor[p[n, x] /. x -> x - 1/x]]; Table[Expand[f1[n, x]], {n, 0, z/4}]
t = Flatten[Table[CoefficientList[f1[n, x], x], {n, 0, z/4}]]
CROSSREFS
Cf. A230003.
Sequence in context: A056008 A074830 A182983 * A287692 A208889 A127750
KEYWORD
tabf,sign,easy
AUTHOR
Clark Kimberling, Nov 07 2013
STATUS
approved

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Last modified December 7 08:27 EST 2023. Contains 367645 sequences. (Running on oeis4.)