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a(n) = 32*(2^n + 1).
5

%I #21 Sep 08 2022 08:45:51

%S 64,96,160,288,544,1056,2080,4128,8224,16416,32800,65568,131104,

%T 262176,524320,1048608,2097184,4194336,8388640,16777248,33554464,

%U 67108896,134217760,268435488,536870944

%N a(n) = 32*(2^n + 1).

%H G. C. Greubel, <a href="/A175163/b175163.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 (3,-2).

%F a(n) = A173786(n+5, 5).

%F a(n) = 3*a(n-1) - 2*a(n-2), a(0)=64, a(1)=96. - _Vincenzo Librandi_, Dec 28 2010

%F G.f.: 32*(2 - 3*x)/((1 - x)*(1 - 2*x)). - _Chai Wah Wu_, Jul 24 2020

%F E.g.f.: 32*(exp(2*x) + exp(x)). - _G. C. Greubel_, Jul 08 2021

%t 32*(2^Range[0,40] + 1) (* _G. C. Greubel_, Jul 08 2021 *)

%o (Magma) I:=[64,96]; [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..41]]; // _G. C. Greubel_, Jul 08 2021

%o (Sage) [32*(2^n +1) for n in (0..40)] # _G. C. Greubel_, Jul 08 2021

%Y Sequences of the form m*(2^n + 1): A000051 (m=0), A052548 (m=2), A140504 (m=4), A153973 (m=6), A231643 (m=5), A175161 (m=8), A175162 (m=16), this sequence (m=32).

%Y Cf. A173786.

%K nonn

%O 0,1

%A _Reinhard Zumkeller_, Feb 28 2010