[seqfan] Re: Suggestions for A300000 ?

Sean A. Irvine sairvin at gmail.com
Thu Feb 22 23:42:17 CET 2018


I have a potential candidate for A300000.  A triangle based on J. H.
Conway's values from A007972 to A007975.  Essentially these sequences are
about how many permutations of 1,2,...n can be reached in a given number of
"block reversals" where a block reversal consists of reversing 2 or more
consecutive values in the permutation.  I'll be extending some of those
sequences soon with extra values, but a triangle for this problem (which I
don't think is currently present in the OEIS) starts:

1
1, 1
1, 3, 2
1, 6, 15, 2
1, 10, 52, 55, 2

Each row sums to n!, T(n,k), k>=0, is the number of permutations of length
n requiring k block-reversals to reach when starting from 1,2,...n.

Actually I'm not yet sure that this continues as a triangle, but it seems
likely.  There are conjectured formulas for column 2 (2, 15, 52, ...) in
A007972.

Sean.

On 7 February 2018 at 05:55, Neil Sloane <njasloane at gmail.com> wrote:

> Dear Seq Fans,
>
> We will soon reach A-number A300000.  If you see any sequences worthy of
> this honor in the next week or two, please send me an email.
>
> A sequence that has already been approved can be renumbered as A300000.
>
> If one of you has a chance to reserve the A-numbers A300000 through
> A300009, say, please grab them and let me know!
>
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
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>


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