[seqfan] Number Of Such Permutations
Leroy Quet
q1qq2qqq3qqqq at yahoo.com
Tue Jan 5 17:12:31 CET 2010
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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