A145766 Partial sums of A020988.

0, 2, 12, 54, 224, 906, 3636, 14558, 58248, 233010, 932060, 3728262, 14913072, 59652314, 238609284, 954437166, 3817748696, 15270994818, 61083979308, 244335917270, 977343669120, 3909374676522, 15637498706132, 62549994824574

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Oct 18 2008

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Hacène Belbachir and El-Mehdi Mehiri, Enumerating moves in the optimal solution of the Tower of Hanoi, arXiv:2210.08657 [math.CO], 2022.
• Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Crossrefs

Cf. A014825, A020988.

Programs

Mathematica

lst={}; s=0; Do[s+=(s+=n+s); AppendTo[lst,s],{n,0,5!}]; lst
Accumulate[LinearRecurrence[{5,-4},{0,2},30]] (* or *) LinearRecurrence[ {6,-9,4},{0,2,12},30] (* Harvey P. Dale, Sep 25 2013 *)

Formula

a(n) = Sum_{i=0..n} A020988(i). a(n+1)-a(n)=A020988(n+1).

a(n) = 2*(4^(n+1)-3n-4)/9 = 2*A014825(n). - R. J. Mathar, Oct 21 2008

G.f.: 2*x/((1-x)^2*(1-4*x)). [Colin Barker, Jan 11 2012]

a(n) = 6*a(n-1)-9*a(n-2)+4*a(n-3), for n>2, with {a(k)}={0,2,12}, k=0,1,2. - L. Edson Jeffery, Mar 01 2012

Extensions

Edited by R. J. Mathar, Oct 21 2008