Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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