A074604 a(n) = 2^n + 9^n.

2, 11, 85, 737, 6577, 59081, 531505, 4783097, 43046977, 387421001, 3486785425, 31381061657, 282429540577, 2541865836521, 22876792471345, 205891132127417, 1853020188917377, 16677181699797641, 150094635297261265

Offset: 0

Author

Robert G. Wilson v, Aug 25 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 (11,-18).

Crossrefs

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

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

Programs

Magma

[2^n + 9^n: n in [0..35]]; // Vincenzo Librandi, Apr 30 2011

Mathematica

Table[2^n + 9^n, {n, 0, 25}]
LinearRecurrence[{11,-18},{2,11},26] (* Harvey P. Dale, Feb 28 2022 *)

SageMath

[2^n+9^n for n in range(31)] # G. C. Greubel, Jan 16 2024

Formula

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

a(n) = 11*a(n-1) - 18*a(n-2), with a(0) = 2, a(1) = 11.

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

G.f.: 1/(1-2*x) + 1/(1-9*x).

E.g.f.: exp(2*x) + exp(9*x). (End)