A058922 a(n) = n*2^n - 2^n = 2^n*(n-1).

0, 4, 16, 48, 128, 320, 768, 1792, 4096, 9216, 20480, 45056, 98304, 212992, 458752, 983040, 2097152, 4456448, 9437184, 19922944, 41943040, 88080384, 184549376, 385875968, 805306368, 1677721600, 3489660928, 7247757312, 15032385536, 31138512896, 64424509440, 133143986176

Offset: 1

Author

N. J. A. Sloane, Jan 12 2001

Keywords

• nonn
• easy

Comments

A hierarchical sequence (S(W'2{2}*c) - see A059126).

Links

• Harry J. Smith, Table of n, a(n) for n = 1..200
• Jonas Wallgren, Hierarchical sequences, 2001.
• Index entries for linear recurrences with constant coefficients, signature (4,-4).

Crossrefs

A001787(n) = a(n+1)/4. A073346(n, n-2) = a(n-2).

Cf. A000337. - Omar E. Pol, Feb 22 2010

Programs

Haskell

a058922 n = (n - 1) * 2 ^ n
a058922_list = zipWith (*) [0..] $ tail a000079_list
-- Reinhard Zumkeller, Jul 11 2014

Mathematica

Table[n*2^n-2^n,{n,100}] (* Vladimir Joseph Stephan Orlovsky, Jan 15 2011 *)

PARI

a(n) = { n*2^n - 2^n } \\ Harry J. Smith, Jun 24 2009

Formula

a(n) = -det(M(n+1)) where M(n) is the n X n matrix with m(i,i)=1, m(i,j)=-i/j for i != j. - Benoit Cloitre, Feb 01 2003

With offset 0, this is 4n*2^(n-1), the binomial transform of 4n. - Paul Barry, May 20 2003

a(1)=0, a(n) = 2*a(n-1) + 2^n for n>1. - Philippe Deléham, Apr 20 2009

a(n) = A000337(n) - 1. - Omar E. Pol, Feb 22 2010

From R. J. Mathar, Mar 01 2010: (Start)

a(n)= 4*a(n-1) - 4*a(n-2).

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

From Amiram Eldar, Jan 12 2021: (Start)

Sum_{n>=2} 1/a(n) = log(2)/2.

Sum_{n>=2} (-1)^n/a(n) = log(3/2)/2. (End)