OFFSET
1,2
COMMENTS
A hierarchical sequence (S(W'2{2}*c) - see A059126).
The score associated with a 2^n-tile in Gabriele Cirulli's popular video game "2048", if only 2's appear. - Johann Peters, Oct 17 2025
For n>=2, also the number of minimum connected dominating sets in the (n-1)-necklace graph. - Eric W. Weisstein, Feb 17 2026
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..200
Gabriele Cirulli, Play 2048.
Jonas Wallgren, Hierarchical sequences, 2001.
Eric Weisstein's World of Mathematics, Minimum Dominating Set.
Eric Weisstein's World of Mathematics, Necklace Graph.
Index entries for linear recurrences with constant coefficients, signature (4,-4).
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)
From Enrique Navarrete, Dec 31 2025: (Start)
a(n) = Sum_{k=1..n} A001787(k) - 1.
E.g.f.: 1 + (2*x - 1)*exp(2*x). (End)
MATHEMATICA
Table[n*2^n-2^n, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jan 15 2011 *)
PROG
(PARI) a(n) = { n*2^n - 2^n } \\ Harry J. Smith, Jun 24 2009
(Haskell)
a058922 n = (n - 1) * 2 ^ n
a058922_list = zipWith (*) [0..] $ tail a000079_list
-- Reinhard Zumkeller, Jul 11 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 12 2001
STATUS
approved