[seqfan] Re: simple sequence not in OEIS

Alexander P-sky apovolot at gmail.com
Mon Jul 23 15:25:22 CEST 2012

```Yes WolframAlpha confirms the G.F. and gives more terms

1, 1, 2, 6, 12, 25, 57, 124, 268, 588, 1285, 2801, 6118, 13362, 29168,
63685, 139057, 303608, 662888, 1447352, 3160121, 6899745, 15064810,
32892270, 71816436, 156802881, 342360937, 747505396, 1632091412,
3563482500, 7780451037, 16987713169, 37090703118, 80983251898,
176817545560, 386060619981, 842918624353, 1840415132912,
4018333162768, 8773564788720, 19156061974577, 41825041384513,
91320130888018, 199386922984982, 435338240001116, 950510597034665, ...

On 7/23/12, David Scambler <dscambler at bmm.com> wrote:
> Number of permutations of 1..n for which the partial sum of signed
> displacements does not exceed 2.
>
> e.g. n=5
>
> s(i)             3  1  4  2  5
> s(i)-i           2 -1  1 -2  0
> partial sum      2  1  2  0  0   // max = 2 so counted
>
> s(i)             3  1  4  5  2
> s(i)-i           2 -1  1  1 -3
> partial sum      2  1  2  3  0   // max = 3 so not counted
>
> a(n) = 1, 1, 2, 6, 12, 25, 57, 124, 268, 588, 1285, 2801, 6118, 13362, ...
>
> seems to be
> g.f. 1/(1-n-n^2-3*n^3-n^4)
>
>
> dave
>
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>
```