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
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (13,-36).
Programs
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Magma
[2^(2*n+1) + 3^(2*n+1): n in [0..30]]; // G. C. Greubel, Mar 11 2023
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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
Comments