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.
%I A013730 #53 Nov 03 2024 12:24:44
%S A013730 2,16,128,1024,8192,65536,524288,4194304,33554432,268435456,
%T A013730 2147483648,17179869184,137438953472,1099511627776,8796093022208,
%U A013730 70368744177664,562949953421312,4503599627370496,36028797018963968,288230376151711744,2305843009213693952,18446744073709551616
%N A013730 a(n) = 2^(3*n+1).
%C A013730 1/2 + 1/16 + 1/128 + 1/1024 + ... = 4/7. - _Gary W. Adamson_, Aug 29 2008
%H A013730 Vincenzo Librandi, <a href="/A013730/b013730.txt">Table of n, a(n) for n = 0..200</a>
%H A013730 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A013730 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (8).
%H A013730 <a href="/index/Di#divseq">Index to divisibility sequences</a>.
%F A013730 From _Philippe Deléham_, Nov 23 2008: (Start)
%F A013730 a(n) = 8*a(n-1), n > 0; a(0)=2.
%F A013730 G.f.: 2/(1-8x). (End)
%F A013730 a(n) = A157176(A016921(n)) = A157176(A016933(n)). - _Reinhard Zumkeller_, Feb 24 2009
%F A013730 From _Amiram Eldar_, May 08 2023: (Start)
%F A013730 Sum_{n>=0} (-1)^n/a(n) = 4/9.
%F A013730 Product_{n>=0} (1 - 1/a(n)) = A132024. (End)
%F A013730 E.g.f.: 2*exp(8*x). - _Stefano Spezia_, May 29 2024
%p A013730 seq(2^(3*n+1),n=0..19); # _Nathaniel Johnston_, Jun 26 2011
%t A013730 Table[2^n, {n, 1, 100, 3}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 14 2011 *)
%t A013730 2^(3 Range[0, 40] + 1) (* _Vladimir Joseph Stephan Orlovsky_, Jun 14 2011 *)
%t A013730 Table[2^(3 n + 1), {n, 0, 20}] (* _Eric W. Weisstein_, Nov 03 2024 *)
%t A013730 2^(3 Range[0, 20] + 1) (* _Eric W. Weisstein_, Nov 03 2024 *)
%t A013730 2^Range[1, 61, 3] (* _Eric W. Weisstein_, Nov 03 2024 *)
%t A013730 LinearRecurrence[{8}, {2}, 20] (* _Eric W. Weisstein_, Nov 03 2024 *)
%t A013730 CoefficientList[Series[2/(1 - 8 x), {x, 0, 20}], x] (* _Eric W. Weisstein_, Nov 03 2024 *)
%o A013730 (Magma) [2^(3*n+1): n in [0..30]]; // _Vincenzo Librandi_, May 04 2011
%o A013730 (PARI) a(n)=2<<(3*n) \\ _Charles R Greathouse IV_, Jun 14 2011
%Y A013730 Cf. A013731, A016921, A016933, A132024, A157176.
%K A013730 nonn,easy
%O A013730 0,1
%A A013730 _N. J. A. Sloane_