A074614 a(n) = 4^n + 9^n.

2, 13, 97, 793, 6817, 60073, 535537, 4799353, 43112257, 387682633, 3487832977, 31385253913, 282446313697, 2541932937193, 22877060890417, 205892205836473, 1853024483819137, 16677198879535753, 150094704016475857

Offset: 0

Author

Robert G. Wilson v, Aug 26 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 (13,-36).

Crossrefs

Cf. A000051, A034472, A034474, A034491, A052539, A062394, A062395.

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

Bisection of A007689 (even-indexed members).

Programs

Magma

[4^n+9^n: n in [0..30]]; // G. C. Greubel, Mar 10 2023

Mathematica

Table[4^n + 9^n, {n, 0, 25}]
LinearRecurrence[{13,-36},{2,13},30] (* Harvey P. Dale, Aug 11 2017 *)

PARI

a(n)=4^n+9^n \\ Charles R Greathouse IV, Jul 01 2016

SageMath

[4^n+9^n for n in range(31)] # G. C. Greubel, Mar 10 2023

Formula

a(n) = 2^(2*n) + 3^(2*n).

G.f.: (2-13*x)/((1-4*x)*(1-9*x)).

E.g.f.: e^(4*x) + e^(10*x). - Mohammad K. Azarian, Jan 11 2009

a(n) = 13*a(n-1) - 36*a(n-2) with a(0)=2, a(1)=13. - Vincenzo Librandi, Jul 21 2010