A231148 Array of coefficients of numerator polynomials of the rational function p(n, x - 1/x), where p(n,x) = (x^n - 1)/(x - 1).

1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 2, -1, -2, 1, 1, 1, -1, -3, 2, 5, -2, -3, 1, 1, -1, 1, 4, -3, -8, 5, 8, -3, -4, 1, 1, 1, -1, -5, 4, 12, -8, -15, 8, 12, -4, -5, 1, 1, -1, 1, 6, -5, -17, 12, 27, -15, -27, 12, 17, -5, -6, 1, 1, 1, -1, -7, 6, 23, -17, -44

Offset

1,12

Links

Table of n, a(n) for n=1..71.

Example

First 4 rows:
1
-1 1 1
1 -1 -1 1 1
-1 1 2 -1 -2 1 1
First 4 polynomials: 1, -1 + x + x^2, 1 - x - x^2 + x^3 + x^4

Mathematica

z = 60; p[n_, x_] := p[x] = (x^n - 1)/(x - 1); Table[p[n, x], {n, 1, 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}]
Flatten[Table[CoefficientList[f1[n, x], x], {n, 1, z/4}]]

Crossrefs

Cf. A231147.

Sequence in context: A048138 A165022 A030338 * A266649 A159847 A327489

Adjacent sequences: A231145 A231146 A231147 * A231149 A231150 A231151

Keyword

tabf,sign,easy

Author

Clark Kimberling, Nov 05 2013

Status

approved