Tower of Hanoi

Creighton Dement crowdog at crowdog.de
Sat Jul 16 23:54:43 CEST 2005

```Dear Seqfans,

A variant of Zak's sequence
http://www.research.att.com/projects/OEIS?Anum=A086348
is
http://www.research.att.com/projects/OEIS?Anum=A110048
and may be of interest as it apparently relates his "chessboard
sequence" to Pell numbers. To Zak: I began the search for your sequence
http://www.research.att.com/projects/OEIS?Anum=A086346  (...landing in a
corner cell) with the help of FAMP today. I've not had any luck finding
it yet.

In reference to the "Tower of Hanoi", sequences A005665, A077846, and
A000001, below, are in the same batch of (16) floretion base sequences
(see comment) and this may also be of interest:

%S A000001 -1, 1, 3, 11, 31, 87, 239, 655, 1791, 4895, 13375, 36543,
99839, 272767, 745215, 2035967, 5562367, 15196671, 41518079, 113429503,
309895167, 846649343, 2313089023, 6319476735, 17265131519, 47169216511,
128868696063, 352075825151, 961889042431, 2627929735167, 7179637555199
%N A000001 a(n+3) = 3*a(n+2) - 2*a(n), a(0) = -1, a(1) = 1, a(2) = 3
%C A000001 In reference to the program code, "ibasek" corresponds to the
floretion 'ik'. Sequences in this same batch are "kbase" = A005665
(Tower of Hanoi with cyclic moves only.) and "ibase" = A077846.
%F A000001 a(n) = A028860(n+2)-1, G.f. (-1+4*x)/((x-1)*(2*x^2+2*x-1))
%p A000001 seriestolist(series((-1+4*x)/((x-1)*(2*x^2+2*x-1)), x=0,31));
-or- Floretion Algebra Multiplication Program, FAMP Code:
2ibaseksumseq[A*B] with A =  + 'i + 'ii' + 'ij' + 'ik' and B =  + .5'i +
.5'j - .5'k + .5i' - .5j' + .5k' + .5'ij' + .5'ik' - .5'ji' - .5'ki' ;
Sumtype is set to:sum[(Y[0], Y[1], Y[2]),mod(3)
%Y A000001 A005665, A077846, A028860
%O A000001 0
%K A000001 ,easy,sign,
%A A000001 Creighton Dement (crowdog at crowdog.de), Jul 16 2005

Also, I've uploaded a few of my first attempts at ray-tracing a plot of
floretion integer sequences and scattered these around vaious points of
my homepage http://www.crowdog.de

Sincerely,
Creighton

```