cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A175161 a(n) = 8*(2^n + 1).

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%I A175161 #27 Sep 08 2022 08:45:51
%S A175161 16,24,40,72,136,264,520,1032,2056,4104,8200,16392,32776,65544,131080,
%T A175161 262152,524296,1048584,2097160,4194312,8388616,16777224,33554440,
%U A175161 67108872,134217736,268435464,536870920,1073741832,2147483656,4294967304,8589934600,17179869192
%N A175161 a(n) = 8*(2^n + 1).
%H A175161 G. C. Greubel, <a href="/A175161/b175161.txt">Table of n, a(n) for n = 0..1000</a>
%H A175161 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A175161 a(n) = A173786(n+3, 3).
%F A175161 a(n) = A175166(2*n)/A159741(n) for n > 0.
%F A175161 a(n) = 3*a(n-1) -2*a(n-2) with a(0)=16, a(1)=24. - _Vincenzo Librandi_, Dec 28 2010
%F A175161 G.f.: 8*(2 - 3*x)/((1-x)*(1-2*x)). - _Chai Wah Wu_, Jun 20 2020
%F A175161 a(n) = 8 * A000051(n). - _Alois P. Heinz_, Jun 20 2020
%F A175161 E.g.f.: 8*(exp(2*x) + exp(x)). - _G. C. Greubel_, Jul 08 2021
%t A175161 8*(2^Range[0, 40] + 1) (* _G. C. Greubel_, Jul 08 2021 *)
%t A175161 LinearRecurrence[{3,-2},{16,24},40] (* _Harvey P. Dale_, Feb 10 2022 *)
%o A175161 (Magma) I:=[16,24]; [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 A175161 (Sage) [8*(2^n +1) for n in (0..40)] # _G. C. Greubel_, Jul 08 2021
%Y A175161 Sequences of the form m*(2^n + 1): A000051 (m=1), A052548 (m=2), A140504 (m=4), A153973 (m=6), A231643 (m=5), this sequence (m=8), A175162 (m=16), A175163 (m=32).
%Y A175161 Cf. A159741, A173786, A175166.
%K A175161 nonn,easy
%O A175161 0,1
%A A175161 _Reinhard Zumkeller_, Feb 28 2010