[seqfan] Re: A007286 and A007289 have exactly the same name.

Maximilian Hasler maximilian.hasler at gmail.com
Sun Apr 28 15:01:05 CEST 2013


FWIW :

Sequence
A007286 <https://oeis.org/A007286>*Number* *of* *alternating* *3*-*signed* *
permutations*.
1, 1, 5, 26, 205, 1936, 22265, 297296, 4544185, 78098176, 1491632525,
31336418816, ...
has

E.g.f.: ( sin x + cos 2x ) / cos 3x.

The e.g.f.  (sin(x) + cos(3*x)) / cos(4*x)
produces the sequence
A006873 Number of alternating 4-signed permutations.
1, 1, 7, 47, 497, 6241, 95767, 1704527, 34741217, 796079041, 20273087527,
567864586607, 17352768515537, 574448847467041, 20479521468959287,
782259922208550287, 31872138933891307457,...


OTOH, Sequence
A007289 <https://oeis.org/A007289>*Number* *of* *alternating* *3*-*signed* *
permutations*.
1, 2, 8, 46, 352, 3362, 38528, 515086, 7869952, 135274562, 2583554048,
54276473326, ...
has

E.g.f.: (sin(2*x) + cos(x)) / cos(3*x).


and the
e.g.f. (sin(3*x) + cos(x)) / cos(4*x)
produces the sequence
1, 3, 15, 117, 1185, 15123, 230895, 4116837, 83860545, 1921996323,
48942778575, 1370953667157, 41893214676705, 1386843017916723,
49441928730798255, 1888542637550347077, 76946148390480577665,...
which was not yet in OEIS. (Now proposed as draft.)


Maximilian


On Sun, Apr 28, 2013 at 8:06 AM, Peter Luschny <peter.luschny at gmail.com>wrote:

> http://oeis.org/search?q=id%3AA007286|id%3AA007289
>
> A007286 and A007289 have exactly the same name
> "Number of alternating 3-signed permutations".
> This is a little confusing. Perhaps some clarification could be added?
>
> Peter
>
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> Seqfan Mailing list - http://list.seqfan.eu/
>


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