Two ordering problems

[franktaw at netscape.net]

The property you need is similar to that for a Beatty sequence.  The 
position
of the nth X (or Y) in the sequence will be floor(a*n+c) for some a and 
c.

Franklin T. Adams-Watters

-----Original Message-----
From: David Wilson <dwilson at gambitcomm.com>

Max Alekseyev wrote: 
> It appears that the sequence is good iff the number of Y (resp. X) 
> symbols between any two neighboring X (resp. Y) symbols either equals 
> an integer constant or varies between some two consecutive integer 
> values. 
> In the aforementioned sample sequence 
> X,Y,X,Y,X,X,Y,X,Y,X,X,Y,... 
> the distance between every two neighboring X's is 0 or 1 and the 
> distance between every two neighboring Y's is 1 or 2. 
> 
> With this characterization in mind, it is easy to compute the number 
> of good sequences of length n. 
>
Your observation is certainly a property of good sequences, indeed the
distance between any two adjacent X's will always be k or k+1 for some 
k
(similarly for adjacent Y's). This is necessary for a good sequence, 
but
not sufficient. For example 
 
X,Y,X,Y,X,Y,X,X,Y,X,X 
 
is not good. 





Dear Sequence Fans,

There are now three new web pages to use when sending in:

1.  A new sequence
2.  An addition to an existing sequence
3.  A b-file

See the old "Submit new seq. or comment" page for the links.
Please use the new pages rather than the old page!
This will make maintaining the OEIS a lot easier.

But these pages are new - let me know
if you find any bugs!

Thanks

Neil