A138233 a(n) = 2^(2*n+1) + 3^(2*n+1).

5, 35, 275, 2315, 20195, 179195, 1602515, 14381675, 129271235, 1162785755, 10462450355, 94151567435, 847322163875, 7625731702715, 68630914235795, 617675543767595, 5559069156490115, 50031579458738075, 450284043329950835

Offset: 0

Author

Reinhard Zumkeller, Mar 07 2008

Keywords

• nonn

Comments

Subsequence of A008587.

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. A008587, A096951, A138199.

Programs

Magma

[2^(2*n+1) + 3^(2*n+1): n in [0..30]]; // G. C. Greubel, Mar 11 2023

Mathematica

LinearRecurrence[{13, -36},{5, 35},19] (* Ray Chandler, Jul 14 2017 *)
2^#+3^#&/@(2*Range[0,20]+1) (* Harvey P. Dale, Sep 25 2019 *)

SageMath

[2^(2*n+1) + 3^(2*n+1) for n in range(31)] # G. C. Greubel, Mar 11 2023

Formula

a(n) = 5*A096951(n).

a(n+1) = 4*a(n) + 5*3^(2*n+1), a(0) = 5.

O.g.f.: 5*x*(7-36*x)/((1-4*x)*(1-9*x)). - R. J. Mathar, Apr 24 2008

E.g.f.: 2*exp(4*x) + 3*exp(9*x). - G. C. Greubel, Mar 11 2023