Closed form expression for A288208

Asked Feb 25 '25 at 15:57

Active Mar 02 '25 at 10:10

Viewed 286 times

Trying to resolve my last question, I stumbled on this sequence, A288208, which resolves the case $k=3$. I see that there are various codes proposed to compute the sequence, but there isn't a closed form expression, or even a recurrence relation (like the ones for the simpler Hertzsprung's problem, see A002464).

Is it possible to obtain it?

Now posted on https://mathoverflow.net/questions/488706/closed-form-expression-for-the-enumeration-of-permutations-with-no-fixed-points

edited Mar 02 '25 at 10:10

asked Feb 25 '25 at 15:57

user967210

1,464
5
15

It might be helpful to link to the original Mathematics Stack Exchange post that inspired this OEIS entry. – Paul Sinclair Feb 28 '25 at 18:30
2

I would actually just rewrite this as a separate, self-contained question. Let $A_n$ be the number of permutations $\pi$ of $[n]={1,2,\ldots,n}$ such that $\pi(i)\neq i$ for all $i \in [n]$ and $|\pi(i+1) - \pi(i)| > 1$ for all $i \in [n-1]$. Can a recurrence relation or closed form be found for $A_n$? – mjqxxxx Feb 28 '25 at 20:40
@mjqxxxx I'll try to post on MO – user967210 Mar 02 '25 at 09:30

Closed form expression for A288208

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