A074605 a(n) = 3^n + 4^n.

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.

Links

B. Berselli, Table of n, a(n) for n = 0..1000. - Bruno Berselli, Jul 20 2010

Index entries for linear recurrences with constant coefficients, signature (7,-12).

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

Crossrefs

Cf. A000051, A007689, A034472, A034474, A034491, A052539, A062394.

Cf. A062395, A062396, A063376, A063481, A074506, A074600..A074624.

Sequence in context: A108152 A024482 A097613 * A292613 A108081 A270785

Adjacent sequences: A074602 A074603 A074604 * A074606 A074607 A074608

Keyword

easy,nonn

Author

Robert G. Wilson v, Aug 25 2002

Status

approved