A322455 Sum of n-th powers of the roots of x^3 - 20*x^2 - 9*x - 1.
3, 20, 418, 8543, 174642, 3570145, 72983221, 1491970367, 30499826474, 623497246004, 12745935328713, 260560681614770, 5326550547499821, 108888803019858063, 2225975576006274419, 45504837297851710768, 930239414944110543194, 19016557810138882535211
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..750
- Index entries for linear recurrences with constant coefficients, signature (20,9,1).
Programs
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Mathematica
CoefficientList[Series[(3 - 40*x - 9*x^2) / (1 - 20*x - 9*x^2 - x^3) , {x, 0, 50}], x] (* Amiram Eldar, Dec 09 2018 *) -
PARI
Vec((3 - 40*x - 9*x^2) / (1 - 20*x - 9*x^2 - x^3) + O(x^20)) \\ Colin Barker, Dec 09 2018
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PARI
polsym(x^3 - 20*x^2 - 9*x - 1, 25) \\ Joerg Arndt, Dec 17 2018
Formula
a(n) = (B*C^3/A^4)^n + (C*A^3/B^4)^n + (A*B^3/C^4)^n.
a(n) = 20*a(n-1) + 9*a(n-2) + a(n-3) for n > 2.
G.f.: (3 - 40*x - 9*x^2) / (1 - 20*x - 9*x^2 - x^3). - Colin Barker, Dec 09 2018
Comments