A074602 a(n) = 2^n + 7^n.

2, 9, 53, 351, 2417, 16839, 117713, 823671, 5765057, 40354119, 282476273, 1977328791, 13841291297, 96889018599, 678223089233, 4747561542711, 33232930635137, 232630514118279, 1628413598172593, 11398895185897431

Offset: 0

Author

Robert G. Wilson v, Aug 25 2002

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-14).

Crossrefs

Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600 - A074624.

Programs

Magma

[2^n + 7^n: n in [0..35]]; // Vincenzo Librandi, Apr 30 2011

Mathematica

Table[2^n + 7^n, {n, 0, 25}]
LinearRecurrence[{9,-14},{2,9},20] (* Harvey P. Dale, May 10 2025 *)

Formula

a(n) = 7*a(n-1) - 2^n = 9*a(n-1) - 14*a(n-2).

From Mohammad K. Azarian, Jan 02 2009: (Start)

G.f.: 1/(1-2*x) + 1/(1-7*x).

E.g.f.: e^(2*x) + e^(7*x). (End)

a(n) = 2*A016130(n)-9*A016130(n-1). - R. J. Mathar, Mar 10 2022