Is sequence A084894 plausible?
Pfoertner, Hugo
Hugo.Pfoertner at muc.mtu.de
Mon Sep 6 10:49:35 CEST 2004
>-----Original Message-----
>From: Brendan McKay [mailto:bdm at cs.anu.edu.au]
>Sent: Monday, September 06, 2004 09:39
>To: seqfan at ext.jussieu.fr
>Subject: Is sequence A084894 plausible?
>
>
>
>ID Number: A084894
>Sequence: 0,0,2,20,112,696,5008,40280,362760,3628504,39916152,
> 479000272,6227017600,8717828,1288,1307674342408,
> 20922789832080,355687427952808,6402373705217304,
> 1216451004073,80704,2432902008173142656
>Name: Number of permutations of length n such that at
>least one absolute
> difference between consecutive elements has a
>distinct partner.
>Comments: a(n)=n!-A006967(n)
>
>I suggest that this sequence is broken as the small values interspersed
>with the large values are impossible. Sequence A006967 (graceful
>permutations) is ok. Graceful permutations are a vanishing fraction
>of all permutations so A084894(n) should be close to n!.
>
>Brendan.
>
Seems to be the usual line-wrap mess when using the submission form
carelessly.
See the FAQ's: "Q: A comma appeared in the middle of a number in my sequence
- why?"
http://www.research.att.com/~njas/sequences/FAQ.html#Z43
The correct sequence should be:
0,0,2,20,112,696,5008,40280,362760,3628504,39916152,
479000272,6227017600,87178281288,1307674342408,
***********
20922789832080,355687427952808,6402373705217304,
121645100407380704,2432902008173142656
******************
The interspersed small values "1288" and "80704" just have to be
concatenated with
the preceding entries to get what the comment says.
Hugo
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