[seqfan] Defining floretion sequences more clearly, and new web links

Robert Munafo mrob27 at gmail.com
Fri Nov 20 04:33:24 CET 2009

Creighton's reply is greatly appreciated. I just wrote back to him to
ask more questions that I think he alone can answer.

I am working on my own floretions web page, it is at
http://mrob.com/pub/math/seq-floretion.html   At present it just
duplicates my earlier message and has links to all the OEIS entries I
found with my Sloandora tool. Once I have something more tangible I'll
improve it.

I definitely think Crieghton's work is valuable, but I also think it
is inaccessible. That was the point of my message, as Franklin T.
Adams-Watters suggested.

Regarding the web links that were deleted in 2005, I think we should
replace them with new links. I have an archive of the OEIS from
December 2005 and can provide NJAS with a list of A-numbers that
contained links to http://www.crowdog.de. There are 244 links in 196
distinct OEIS entries. The lowest A-number was A000045 and the highest
was A112533 (which Creighton submitted on Sep 11 2005). Rather than
link in all of those sequences (I think it is a bit irrelevant in
A000045, for example) perhaps we could start with the sequences
Creighton actually authored.

If this continues to hold my interest I'll probably be able to write
code in a standard language that doesn't rely on custom functions.
Creighton's reply is a good start, and I have the Java source code,
which might help me figure out more of it.

It is clear to me these iteration algorithms are simple enough to
define in an obvious language, without special symbols or terminology.
It does all seem to be defined in the Java Moonlice code.

Creighton's tutorial on how to produce A100545 works -- I have quoted
the relevant part here, with two clarifications. This is a big step in
the right direction!

> From: "N. J. A. Sloane"
>  I agree!  Right now it is trivial for me to add a link to a list of sequences.  (It might not
> be so trivial once we go wiki.)  If someone sends me a list of A-numbers and the link,
> I have a program that will do the rest of the work.

> From: "Creighton Kenneth Dement"
> [...] Let's see how to generate A100545:
> [...] Go to http://www.fumba.eu/sitelayout/floretion.html and, on the list at the right, choose "Basic Fibonacci".

[You also need to select "ves" from the first list -RM]

> You should see that the floretion "E" defined in the above in Prop. 3.3 is automatically set in the top row. The second row contains the numbers (-1,-1,1) which corresponds to the quaternion Y = -'i -'j + 'k
> [...] The next simplest case (using Prop. 3.4) would be to choose Y = -2'i + 'j + 'k - i'

[This means, change the second row to: -2, 1, 1, -1 leaving the rest
of that row blank, then hit Go Python! -RM]

> Scan down the batch of sequences and you should see these lines:
> 2mixseq: [1, 3, 8, 21, 55, 144, 377, 987, 2584, 6765]
> 4mixposseq: [3, 8, 23, 61, 160, 419, 1097, 2872, 7519, 19685]
> 4mixnegseq: [-1, -2, -7, -19, -50, -131, -343, -898, -2351, -6155]

 Robert Munafo  --  mrob.com

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