[seqfan] Re: b-files for apparently matching sequences?

Torleiv.Klove at ii.uib.no Torleiv.Klove at ii.uib.no
Thu Jul 1 08:27:40 CEST 2010

For P(d,d,n) (for each fixed d) explisit generating functions are known, 

T. Kløve, Generating Functions for the Number of Permutations with 
Limited Displacement,
The Electronic Journal of Combinatorics, R104, vol. 16(1), August 14, 2009.

T. Kløve, Spheres of permutations under the infinity norm - Permutations 
with limited displacement,
Reports in Informatics, Dept. of Informatics, Univ. Bergen, Report no. 
376, November 2008.
Online: http://www.ii.uib.no/publikasjoner/texrap/pdf/2008-376.pdf

The generating function gives a recursion of length 

For d up to d=6, this is the shortest possible recursion, and I 
conjecture that this is the case for all d.


Joerg Arndt wrote:
> * Ron Hardin <rhhardin at att.net> [Jun 30. 2010 19:46]:
>> I've put up a catalog of results so far (updated irregularly) for all A B at
>> http://rhhardin.home.mindspring.com/current2.txt
> fine work!
> suggest splitting into auto-named files like A-B.txt
>> if anybody wants to search for a formula.
>> Note that a recurrence is likely to be huge.
>> http://www.research.att.com/~njas/sequences/A72853 has one out to a(n-34)
>> (which recurrence checked correct, by the way; though the a(n) listed is limited by 3 lines to less than 34 terms.)
> I am surprise by the 'size' of this recursion.
> So by
>> [...]
>> A closed from 
>>> for the recurrence for P(A,B,n) would be a nice.
> I hereby mean a procedure to generate a formula  ;-)
> Are you using Knuth 'perms with conditions on prefixes'
> algorithm for enumeration (by generation)?
> hm..., hardly, unless you have overclocked your CPU
> by a truly amazing factor:
> 4 3 100 9276214007544699392817874641185108428600630913087280
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