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) = 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
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Oct 18 2008
EXTENSIONS
Edited by R. J. Mathar, Oct 21 2008
STATUS
approved