A074548 a(n) = 3^n + 4^n + 6^n.

3, 13, 61, 307, 1633, 9043, 51481, 298507, 1751713, 10359523, 61573801, 367168507, 2194090993, 13129397203, 78637382521, 471273075307, 2825447921473, 16943968454083, 101629063565641, 609635780178907

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 (13,-54,72).

Crossrefs

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

Programs

Magma

[3^n + 4^n + 6^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011

Mathematica

Table[3^n + 4^n + 6^n, {n, 0, 21}]
LinearRecurrence[{13,-54,72},{3,13,61},30] (* Harvey P. Dale, Dec 21 2022 *)

Formula

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

G.f.: 1/(1-3*x) + 1/(1-4*x) + 1/(1-6*x).

E.g.f.: exp(3*x) + exp(4*x) + exp(6*x). (End)

a(n) = 13*a(n-1) - 54*a(n-2) + 72*a(n-3).