A018215 a(n) = n*4^n.

0, 4, 32, 192, 1024, 5120, 24576, 114688, 524288, 2359296, 10485760, 46137344, 201326592, 872415232, 3758096384, 16106127360, 68719476736, 292057776128, 1236950581248, 5222680231936, 21990232555520, 92358976733184, 387028092977152, 1618481116086272

Offset: 0

Author

N. J. A. Sloane, Peter Winkler (pw(AT)bell-labs.com)

Keywords

• nonn
• easy

Comments

Bisection of A001787. That is, a(n) = A001787(2*n). - Graeme McRae, Jul 12 2006

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (8,-16).

Crossrefs

Cf. A000302 (4^n), A001787, A002450, A083679.

Row n=4 of A258997.

Programs

Magma

[n*4^n: n in [0..25]]; // Vincenzo Librandi, Jun 01 2011

Mathematica

Table[n 4^n,{n,0,20}] (* or *) LinearRecurrence[{8,-16},{0,4},30] (* Harvey P. Dale, Apr 22 2018 *)

PARI

a(n) = n<<(2*n) \\ David A. Corneth, Apr 22 2018

Formula

G.f.: 4*x/(1-4*x)^2.

E.g.f.: 4*x*exp(4*x).

From Amiram Eldar, Jul 20 2020: (Start)

Sum_{n>=1} 1/a(n) = log(4/3) = A083679.

Sum_{n>=1} (-1)^(n+1)/a(n) = log(5/4). (End)