[seqfan] Re: Energy-limited permutations?
olivier.gerard at gmail.com
Mon Jul 5 18:04:48 CEST 2010
You might want to compare these sequences to
and little variations of it.
and related ones.
You should be able to make one or several triangles.
On Mon, Jul 5, 2010 at 16:34, Ron Hardin <rhhardin at att.net> wrote:
> Quick computation
> %S A000001
> %N A000001 Number of permutations of 1..n with sum (i-p(i))^2 <= n*(n-1)/2
> %S A000002
> %N A000002 Number of permutations of 1..n with sum (i-p(i))^2 <= (n+1)*n/2
> %S A000003
> %N A000003 Number of permutations of 1..n with sum (i-p(i))^2 < n*(n-1)/2
> %S A000004
> %N A000004 Number of permutations of 1..n with sum (i-p(i))^2 < (n+1)*n/2
> Take the energy of a permuation as the sum of the squares of the
> displacements i-p(i).
> What to compare this energy to, to make the count a sequence? Half the sum
> of the elements 1..n, or elements 0..(n-1), is conveniently integer.
> And then you can use <= or < that energy.
> Any others that are not too arbitrary?
> rhhardin at mindspring.com
> rhhardin at att.net (either)
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