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 A018215 #43 Apr 17 2025 03:35:18
%S A018215 0,4,32,192,1024,5120,24576,114688,524288,2359296,10485760,46137344,
%T A018215 201326592,872415232,3758096384,16106127360,68719476736,292057776128,
%U A018215 1236950581248,5222680231936,21990232555520,92358976733184,387028092977152,1618481116086272
%N A018215 a(n) = n*4^n.
%C A018215 Bisection of A001787. That is, a(n) = A001787(2*n). - _Graeme McRae_, Jul 12 2006
%C A018215 All numbers of the form n*4^n+(4^n-1)/3 have the property that they are sums of two squares and also their indices are the sum of two squares. This follows from the identity n*4^n+(4^n-1)/3 = 4*(4*(..(4*(4*n+1)+1)..)+1)+1. - _Artur Jasinski_, Nov 12 2007
%H A018215 Vincenzo Librandi, <a href="/A018215/b018215.txt">Table of n, a(n) for n = 0..300</a>
%H A018215 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-16).
%F A018215 G.f.: 4*x/(1-4*x)^2.
%F A018215 E.g.f.: 4*x*exp(4*x).
%F A018215 From _Amiram Eldar_, Jul 20 2020: (Start)
%F A018215 Sum_{n>=1} 1/a(n) = log(4/3) = A083679.
%F A018215 Sum_{n>=1} (-1)^(n+1)/a(n) = log(5/4). (End)
%t A018215 Table[n 4^n,{n,0,20}] (* or *) LinearRecurrence[{8,-16},{0,4},30] (* _Harvey P. Dale_, Apr 22 2018 *)
%o A018215 (Magma) [n*4^n: n in [0..25]]; // _Vincenzo Librandi_, Jun 01 2011
%o A018215 (PARI) a(n) = n<<(2*n) \\ _David A. Corneth_, Apr 22 2018
%Y A018215 Cf. A000302 (4^n), A001787, A002450, A083679.
%Y A018215 Row n=4 of A258997.
%K A018215 nonn,easy
%O A018215 0,2
%A A018215 _N. J. A. Sloane_, Peter Winkler (pw(AT)bell-labs.com)