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A231147 Array of coefficients of numerator polynomials of the rational function p(n, x + 1/x), where p(n,x) = (x^n - 1)/(x - 1). 2
1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 4, 3, 4, 1, 1, 1, 1, 5, 4, 9, 4, 5, 1, 1, 1, 1, 6, 5, 14, 9, 14, 5, 6, 1, 1, 1, 1, 7, 6, 20, 14, 29, 14, 20, 6, 7, 1, 1, 1, 1, 8, 7, 27, 20, 49, 29, 49, 20, 27, 7, 8, 1, 1, 1, 1, 9, 8, 35, 27, 76, 49, 99, 49, 76, 27, 35, 8, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

LINKS

Table of n, a(n) for n=1..79.

EXAMPLE

First 5 rows:

1

1 1 1

1 1 3 1 1

1 1 4 3 4 1 1

1 1 5 4 9 4 5 1 1

First 3 polynomials: 1, 1 + x + x^2, 1 + x + 3*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. A231148.

Sequence in context: A195768 A016465 A122947 * A046534 A224489 A318933

Adjacent sequences:  A231144 A231145 A231146 * A231148 A231149 A231150

KEYWORD

nonn,tabf,easy

AUTHOR

Clark Kimberling, Nov 05 2013

STATUS

approved

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Last modified September 25 02:16 EDT 2021. Contains 347651 sequences. (Running on oeis4.)