[seqfan] Re: A question about partitions

[Neil Sloane]

William, Roland,  Nice work!

William, Could you send me a version of your proof  in a format that I can
add to A238005?
Roland, same question, although I think I can just use what you sent.

Then I will add a theorem (conjectured by Omar, with two proofs) to A238005,
something like this:

Theorem: a(n) is also the (maximal number of parts in any partition of n
into distinct parts) minus (number of ways to partition n into consecutive
parts), or in other words a(n) =  A003056(n) - A001227(n).

First proof from ...

Second proof from ...

and then I will mark A296509 as "dead".


Best regards
Neil

Neil J. A. Sloane, Chairman, 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



On Sun, Sep 5, 2021 at 8:56 PM William Keith <william.keith at gmail.com>
wrote:

> I used k in two different roles in my explanation of the RHS partitions but
> the list given is correct.  Sorry.
>
> Best,
> William
>
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