[seqfan] Re: Number Of Such Permutations

[Rob Pratt]

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]]) ) ] )]) ] ) ]





_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/