[seqfan] Re: Seqs needing more terms; Like OEIS; San Diego 2013

[Benoît Jubin]

Of course: this inequality is strict (as soon as n>=3). When I wrote
"the 12 extra", I meant "the 12 in addition to your 5".

On Sun, Jun 3, 2012 at 8:39 PM, Neil Sloane <njasloane at gmail.com> wrote:
> PS
>
> Benoit, you said:
>
> The 12 extra partitions we don't get are the ones
> containing either 6 or 7 or 8 or 9 or 10.
> This leads to the observation
> a000041(2n) - a002219(n) >= sum_{k=0..n-1} a000041(k).
>
> Me: I don't think that tells the full story - we are also missing partitions
> like 2^5.
>
> Neil
>
> On Sun, Jun 3, 2012 at 11:09 PM, Benoît Jubin <benoit.jubin at gmail.com>wrote:
>
>> In your comment of A002219, you write that we get all but 5 partitions
>> of 10 (of which you say there are 30). Maybe you use another
>> convention, but to me we get all but 17 partitions of 10, of which
>> there are 42. The 12 extra partitions we don't get are the ones
>> containing either 6 or 7 or 8 or 9 or 10.
>> This leads to the observation
>> a000041(2n) - a002219(n) >= sum_{k=0..n-1} a000041(k)
>> (and the two sides of this inequality could themselves be added to the
>> OEIS).
>>
>> Also, A002219--A002222(0) = A064914(0) = 1.
>>
>> Benoît
>>
>>
>> On Sun, Jun 3, 2012 at 7:41 PM, Neil Sloane <njasloane at gmail.com> wrote:
>> > Dear Seq Fans, 3 items:
>> >
>> > A002219 could use a b-file and A002220-A002222 need more terms (I just
>> found
>> > the 1970 paper that I took them from back in the punched card days). It
>> > seems
>> > that no g.f. or recurrence is known, which is an interesting question.
>> >
>> > The OEIS has a new Facebook page, http://www.facebook.com/OEISF, where
>> you
>> > can "Like" us
>> >
>> > The OEIS will have a booth at the big Amer Math Soc meeting in San Diego,
>> > Jan 9-12, 2013
>> > (this is probably our best opportunity for fundraising in the whole
>> year).
>> > Tony Noe
>> > and I will be there and probably many other sequence lovers. Here is what
>> > Tony said: "Our booth will consist of (a fairly standard) black 8x10
>> > Skyline display. If you have suggestions about what we should display,
>> > please forward your
>> > ideas to Neil or me. I know January sounds like a long time in the
>> future,
>> > but it will be here
>> > before we know it.  For northern hemisphere residents, San Diego can be a
>> > nice respite from Winter.  I know that I am looking forward to it!" We
>> > could also use help - even a few hours -
>> > in manning the booth.
>> >
>> > Neil
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>>
>> _______________________________________________
>>
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>>
>
>
>
> --
> Dear Friends, I have now retired from AT&T. New coordinates:
>
> Neil J. A. Sloane, President, OEIS Foundation
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
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