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%I #27 Oct 18 2022 03:29:28
%S 0,2,12,54,224,906,3636,14558,58248,233010,932060,3728262,14913072,
%T 59652314,238609284,954437166,3817748696,15270994818,61083979308,
%U 244335917270,977343669120,3909374676522,15637498706132,62549994824574
%N Partial sums of A020988.
%H Vincenzo Librandi, <a href="/A145766/b145766.txt">Table of n, a(n) for n = 0..1000</a>
%H Hacène Belbachir and El-Mehdi Mehiri, <a href="https://arxiv.org/abs/2210.08657">Enumerating moves in the optimal solution of the Tower of Hanoi</a>, arXiv:2210.08657 [math.CO], 2022.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4).
%F a(n) = Sum_{i=0..n} A020988(i). a(n+1)-a(n)=A020988(n+1).
%F a(n) = 2*(4^(n+1)-3n-4)/9 = 2*A014825(n). - _R. J. Mathar_, Oct 21 2008
%F G.f.: 2*x/((1-x)^2*(1-4*x)). [_Colin Barker_, Jan 11 2012]
%F 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
%t lst={}; s=0; Do[s+=(s+=n+s); AppendTo[lst,s],{n,0,5!}]; lst
%t Accumulate[LinearRecurrence[{5,-4},{0,2},30]] (* or *) LinearRecurrence[ {6,-9,4},{0,2,12},30] (* _Harvey P. Dale_, Sep 25 2013 *)
%Y Cf. A014825, A020988.
%K nonn
%O 0,2
%A _Vladimir Joseph Stephan Orlovsky_, Oct 18 2008
%E Edited by _R. J. Mathar_, Oct 21 2008