A074506 a(n) = 1^n + 3^n + 4^n.

3, 8, 26, 92, 338, 1268, 4826, 18572, 72098, 281828, 1107626, 4371452, 17308658, 68703188, 273218426, 1088090732, 4338014018, 17309009348, 69106897226, 276040168412, 1102998412178, 4408506864308, 17623567104026

Offset: 0

Author

Robert G. Wilson v, Aug 23 2002

Keywords

• easy
• nonn

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000.
• Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

Crossrefs

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

Equals A074605(n) + 1.

Programs

Mathematica

Table[1^n + 3^n + 4^n, {n, 0, 22}]
LinearRecurrence[{8,-19,12},{3,8,26},30] (* Harvey P. Dale, May 12 2025 *)

Formula

a(n) = 7*a(n-1) - 12*a(n-2) + 6 with a(0)=3, a(1)=8. - Vincenzo Librandi, Jul 19 2010

a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3). - R. J. Mathar, Jul 18 2010

From Mohammad K. Azarian, Dec 26 2008: (Start)

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

E.g.f.: e^x + e^(3*x) + e^(4*x). (End)