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

0,2

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).

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

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 *)

Crossrefs

Cf. A014825, A020988.

Sequence in context: A006738 A212697 A111642 * A181765 A198150 A122676

Adjacent sequences: A145763 A145764 A145765 * A145767 A145768 A145769

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Oct 18 2008

Extensions

Edited by R. J. Mathar, Oct 21 2008

Status

approved