A074549 a(n) = 3^n + 4^n + 7^n.

3, 14, 74, 434, 2738, 18074, 122474, 842114, 5836898, 40635434, 283582874, 1981698194, 13858595858, 96957713594, 678496291274, 4748649600674, 33237268583618, 232647822996554, 1628482704807674, 11399171225541554

Offset: 0

Author

Robert G. Wilson v, Aug 23 2002

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (14,-61,84).

Crossrefs

Cf. A001550, A001576, A034513, A001579, A074501 - A074580.

Programs

Magma

[3^n + 4^n + 7^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011

Mathematica

Table[3^n + 4^n + 7^n, {n, 0, 20}]
LinearRecurrence[{14,-61,84},{3,14,74},20] (* Harvey P. Dale, Jun 11 2024 *)

Formula

From Mohammad K. Azarian, Dec 28 2008: (Start)

G.f.: 1/(1-3*x) + 1/(1-4*x) + 1/(1-7*x).

E.g.f.: exp(3*x) + exp(4*x) + exp(7*x). (End)

a(n) = 14*a(n-1) - 61*a(n-2) + 84*a(n-3).