# [seqfan] Re: simple sequence not in OEIS

Charles Greathouse charles.greathouse at case.edu
Mon Jul 23 23:17:12 CEST 2012

```What do you mean when you say "WolframAlpha confirms the G.F."?  That
it represents this sequence, or just that it matches the terms given?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Jul 23, 2012 at 9:25 AM, Alexander P-sky <apovolot at gmail.com> wrote:
> 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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>>
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>>
>
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>
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```