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A074605
a(n) = 3^n + 4^n.
7
2, 7, 25, 91, 337, 1267, 4825, 18571, 72097, 281827, 1107625, 4371451, 17308657, 68703187, 273218425, 1088090731, 4338014017, 17309009347, 69106897225, 276040168411, 1102998412177, 4408506864307, 17623567104025
OFFSET
0,1
COMMENTS
x^n + y^n = (x+y)*a(n-1) - (x*y)*a(n-2). - Vincenzo Librandi, Jul 19 2010
REFERENCES
L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 14.
FORMULA
a(n) = A074506(n) - 1.
2 + 7*x + 25*x^2 + 91*x^3 + ... n terms = (1 - (4*x)^n)/(1 - 4*x) + (1 - (3*x)^n)/(1 - 3*x). [Jolley] - Gary W. Adamson, Dec 20 2006
From Mohammad K. Azarian, Jan 11 2009: (Start)
G.f.: 1/(1-3*x) + 1/(1-4*x).
E.g.f.: exp(3*x) + exp(4*x). (End)
a(n) = 3*a(n-1) + 4^(n-1). - Bruno Berselli, Jul 20 2010
a(n) = 7*a(n-1) - 12*a(n-2) with a(0)=2, a(1)=7. - Vincenzo Librandi, Jul 19 2010
MATHEMATICA
Table[3^n + 4^n, {n, 0, 25}]
PROG
(PARI) a(n)=3^n+4^n \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [3^n+4^n: n in [0..40]]; // G. C. Greubel, Jan 16 2024
(SageMath) [3^n+4^n for n in range(41)] # G. C. Greubel, Jan 16 2024
KEYWORD
easy,nonn
AUTHOR
Robert G. Wilson v, Aug 25 2002
STATUS
approved