[seqfan] Re: Number Of Such Permutations

[Leroy Quet]

Thanks, Rob.

I myself SHOULD have plugged in the terms I had, with 24 replaced with 23; then tried 24 replaced with 25 if that didn't give anything, since there was a significant chance I erred by 1 or by some small integer.

I would have seen the sequence I needed right off if I bothered to read the comments to the dozens of sequences that match 1,1,3,7,23.

Live and learn.

Thanks,
Leroy Quet

[ ( [ ([( [ ( ([[o0Oo0Ooo0Oo(0)oO0ooO0oO0o]]) ) ] )]) ] ) ]


--- On Tue, 1/5/10, Rob Pratt <Rob.Pratt at sas.com> wrote:

> From: Rob Pratt <Rob.Pratt at sas.com>
> Subject: [seqfan] Re: Number Of Such Permutations
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>, "seqfan at seqfan.eu" <seqfan at seqfan.eu>
> Date: Tuesday, January 5, 2010, 4:46 PM
> I get a(5) = 23, and the sequence
> seems to be:
> http://www.research.att.com/~njas/sequences/A099152
> 
> Rob Pratt
> 
> -----Original Message-----
> From: seqfan-bounces at list.seqfan.eu
> [mailto:seqfan-bounces at list.seqfan.eu]
> On Behalf Of Leroy Quet
> Sent: Tuesday, January 05, 2010 11:13 AM
> To: seqfan at seqfan.eu
> Subject: [seqfan] Number Of Such Permutations
> 
> This email will expose my ignorance, I am sure.
> 
> Let P = (p(1),p(2),p(3),...,p(n)) be a permutation of
> (1,2,3,...,n).
> 
> How many of these permutations, for a given n, are there
> such that for every p(m) equal to k, p(m+j) does not equal
> k+j, for j equal any positive integer, and for all k between
> 1 and n?
> 
> For instance, for n = 4, we count these permutations:
> 2413
> 4213
> 4132
> 4321
> 2431
> 3241
> 3142
> 
> But we would not count, for instance, this permutation:
> 1432
> Because 1+2 = 3 is at a position two to the right of 1.
> 
> I get (by hand, so very likely erroneously) the sequence of
> number of permutations starting (first term is a(1)):
> 1,1,3,7,24
> 
> Searching this with the word "permutations" brings up no
> hits.
> Did I calculate these terms of the sequence correctly?
> 
> Is this sequence in the OEIS as something else not
> obviously related to permutations, perhaps?
> 
> Sorry about my ignorance.
> 
> Thanks,
> Leroy Quet
> 
> 
> [ ( [ ([( [ ( ([[o0Oo0Ooo0Oo(0)oO0ooO0oO0o]]) ) ] )]) ] )
> ]
> 
> 
> 
> 
> 
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