[seqfan] Re: Clarifying A112531

franktaw at netscape.net franktaw at netscape.net
Mon May 19 20:42:51 CEST 2014


I went ahead and added A242628, since we normally include partitions 
with the individual part sizes, not concatenated.

Franklin T. Adams-Watters

-----Original Message-----
From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Mon, May 19, 2014 1:39 pm
Subject: [seqfan] Re: Clarifying A112531


I added A241596 which gives the partitions in this new order, and I 
edited
A112531.
Thanks to everyone for brilliant detective work!


On Mon, May 19, 2014 at 2:16 PM, Neil Sloane <njasloane at gmail.com> 
wrote:

> I just added it, see A241596.
> But I will add Franklin's explanation too
>
>
> On Mon, May 19, 2014 at 2:13 PM, <franktaw at netscape.net> wrote:
>
>> That looks right.
>>
>> This can be defined in terms of the binary expansion. Start with the
>> partition [1]. Now process the bits of the number from right to left,
>> excluding the leading 1. For a zero bit, increase each number in the
>> partition by 1; for a one bit, add a part of size 1.
>>
>> For example, n=11, binary 1011, we get 1 -> 11 -> 111 -> 222. I will 
add
>> this sequence.
>>
>>
>> Franklin T. Adams-Watters
>>
>> -----Original Message-----
>> From: Aai <agroeneveld400 at gmail.com>
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Sent: Mon, May 19, 2014 12:51 pm
>> Subject: [seqfan] Re: Clarifying A112531
>>
>>
>> The partitions expand as follows IMO:
>>
>> 1
>> 2 11
>> 3 22 21 111
>> 4 33 32 222 31 221 211 1111
>> etc.
>>
>> A two step next subsequence of partions based on the previous sub:
>>
>> first:  increment every digit of the partitons by 1
>> second: append a 1 to every partitons
>>
>> e.g. we have:
>>
>> 3 22 21 111
>>
>> then the next subsequence of partitions will be:
>>
>> 4 33 32 222
>> followed by
>>
>> 31 221 211 1111
>>
>> combined to
>>
>> 4 33 32 222 31 221 211 1111
>>
>>
>>
>>
>>
>> On 19-05-14 09:09, Peter Luschny wrote:
>>
>>> Please help clarifying the definition of the triangular array
>>> http://oeis.org/A112531
>>>
>>> Peter
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>
>> --
>> Met vriendelijke groet,
>> @@i = Arie Groeneveld
>>
>>
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>>
>>
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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.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>


--
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.
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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