A074610 a(n) = 3^n + 9^n.

2, 12, 90, 756, 6642, 59292, 532170, 4785156, 43053282, 387440172, 3486843450, 31381236756, 282430067922, 2541867422652, 22876797237930, 205891146443556, 1853020231898562, 16677181828806732, 150094635684419610

Offset: 0

Author

Robert G. Wilson v, Aug 25 2002

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-27).

Crossrefs

Cf. A000051, A007689, A025551, A034472, A034474, A034491, A052539.

Cf. A062394, A062395, A062396, A063376, A063481, A074600..A074624.

Programs

Magma

[3^n+9^n: n in [0..30]]; // G. C. Greubel, Jan 13 2024

Mathematica

Table[3^n + 9^n, {n, 0, 25}]
LinearRecurrence[{12,-27},{2,12},20] (* Harvey P. Dale, May 18 2023 *)

SageMath

[3^n+9^n for n in range(31)] # G. C. Greubel, Jan 13 2024

Formula

From Mohammad K. Azarian, Jan 11 2009: (Start)

G.f.: 1/(1-3*x) + 1/(1-9*x).

E.g.f.: exp(3*x) + exp(9*x). (End)

a(n) = 12*a(n-1) - 27*a(n-2) with a(0)=2, a(1)=12. - Vincenzo Librandi, Jul 21 2010

a(n) = 2*A025551(n). - G. C. Greubel, Jan 13 2024