A001579 a(n) = 3^n + 5^n + 6^n.
3, 14, 70, 368, 2002, 11144, 63010, 360248, 2076802, 12050504, 70290850, 411802328, 2421454402, 14282991464, 84472462690, 500716911608, 2973740844802, 17689728038024, 105375041354530, 628434388600088
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Henri W. Gould, The Girard-Waring power sum formulas for symmetric functions and Fibonacci sequences, The Fibonacci Quarterly, 37(2):135-140, 1999.
- Index entries for linear recurrences with constant coefficients, signature (14,-63,90).
Programs
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Magma
[3^n + 5^n + 6^n: n in [0..20]]; // Vincenzo Librandi, May 20 2011
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Mathematica
Table[3^n + 5^n + 6^n, {n, 0, 20}] LinearRecurrence[{14,-63,90},{3,14,70},20] (* Harvey P. Dale, Jun 17 2021 *) -
PARI
a(n)=3^n+5^n+6^n \\ Charles R Greathouse IV, Jun 10 2011
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Python
def a(n): return 3**n + 5**n + 6**n print([a(n) for n in range(20)]) # Michael S. Branicky, Mar 14 2021
Formula
From Mohammad K. Azarian, Dec 26 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-5*x) + 1/(1-6*x).
E.g.f.: e^(3*x) + e^(5*x) + e^(6*x). (End)