A074607 a(n) = 3^n + 6^n.

2, 9, 45, 243, 1377, 8019, 47385, 282123, 1686177, 10097379, 60525225, 362974203, 2177313777, 13062288339, 78368947065, 470199333483, 2821152954177, 16926788584899, 101560344088905, 609360902271963, 3656161926847377

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 (9,-18).

Crossrefs

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

Programs

Magma

[3^n + 6^n: n in [0..35]]; // Vincenzo Librandi, Apr 30 2011

Mathematica

Table[3^n + 6^n, {n, 0, 25}]

SageMath

[3^n+6^n for n in range(41)] # G. C. Greubel, Jan 14 2024

Formula

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

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

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

a(n) = 9*a(n-1) - 18*a(n-2) with a(0)=2, a(1)=9. - Vincenzo Librandi, Jul 21 2010

G.f.: G(0), where G(k)= 1 + 2^k/(1 - 3*x/(3*x + 2^k/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 22 2013