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A340849 a(n) = A001045(n) + A052928(n). 0
0, 1, 3, 5, 9, 15, 27, 49, 93, 179, 351, 693, 1377, 2743, 5475, 10937, 21861, 43707, 87399, 174781, 349545, 699071, 1398123, 2796225, 5592429, 11184835, 22369647, 44739269, 89478513, 178956999, 357913971, 715827913 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
a(2*n) is divisible by 3.
a(3*n+2) is divisible by 3.
a(n) is the minimum number of moves to solve a Towers of Hanoi puzzle with 4 pegs and n disks where a disk cannot move away from the destination peg (or symmetrically, a disk cannot return to the initial peg). - Woosuk Kwak, Jan 25 2024
LINKS
Woosuk Kwak, 1+3 Towers of Hanoi, Puzzling Stack Exchange.
FORMULA
a(n+1) - 2*a(n) = -A109613(n-2), for a(0)=0, a(1)=1. a(n) + a(n+1) = A100314(n).
a(n+1) - a(n) = A128209(n) for n >= 0.
a(n+2) = 1 + 2*A086445(n). - Hugo Pfoertner, Jan 24 2021
From Woosuk Kwak, Jan 25 2024: (Start)
a(n) = n + floor(2^n/3).
a(n) = n + A000975(n-1) for n >= 1. (End)
MATHEMATICA
LinearRecurrence[{3, -1, -3, 2}, {0, 1, 3, 5}, 32] (* Robert P. P. McKone, Jan 28 2021 *)
CROSSREFS
Sequence in context: A017913 A307677 A140428 * A027154 A217350 A210844
KEYWORD
nonn
AUTHOR
Paul Curtz, Jan 24 2021
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)