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

%I #12 Mar 11 2023 08:14:42

%S 5,35,275,2315,20195,179195,1602515,14381675,129271235,1162785755,

%T 10462450355,94151567435,847322163875,7625731702715,68630914235795,

%U 617675543767595,5559069156490115,50031579458738075,450284043329950835

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

%C Subsequence of A008587.

%H G. C. Greubel, <a href="/A138233/b138233.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (13,-36).

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

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

%F O.g.f.: 5*x*(7-36*x)/((1-4*x)*(1-9*x)). - _R. J. Mathar_, Apr 24 2008

%F E.g.f.: 2*exp(4*x) + 3*exp(9*x). - _G. C. Greubel_, Mar 11 2023

%t LinearRecurrence[{13, -36},{5, 35},19] (* _Ray Chandler_, Jul 14 2017 *)

%t 2^#+3^#&/@(2*Range[0,20]+1) (* _Harvey P. Dale_, Sep 25 2019 *)

%o (Magma) [2^(2*n+1) + 3^(2*n+1): n in [0..30]]; // _G. C. Greubel_, Mar 11 2023

%o (SageMath) [2^(2*n+1) + 3^(2*n+1) for n in range(31)] # _G. C. Greubel_, Mar 11 2023

%Y Cf. A008587, A096951, A138199.

%K nonn

%O 0,1

%A _Reinhard Zumkeller_, Mar 07 2008