A074611 a(n) = 4^n + 5^n.

2, 9, 41, 189, 881, 4149, 19721, 94509, 456161, 2215269, 10814201, 53022429, 260917841, 1287811989, 6371951081, 31591319949, 156882857921, 780119322309, 3883416742361, 19348364235069, 96466943268401, 481235204714229

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,-20).

Crossrefs

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

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

Programs

Magma

[4^n + 5^n: n in [0..30]]; // Vincenzo Librandi, Feb 06 2013

Mathematica

Table[4^n + 5^n, {n, 0, 25}]
CoefficientList[Series[1/(1 - 4 x) + 1/(1 - 5 x), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 06 2013 *)

SageMath

[4^+5^n for n in range(31)] # G. C. Greubel, Jan 13 2024

Formula

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

G.f.: 1/(1-4*x) + 1/(1-5*x).

E.g.f.: exp(4*x) + exp(5*x). (End)

a(n) = 9*a(n-1) - 20*a(n-2), with n>1, a(0)=2, a(1)=9. - Vincenzo Librandi, Jul 21 2010