[seqfan] Re: Clarifying A112531

[franktaw at netscape.net]

It turns out that there is a close relationship between A242628 and 
A125106: each is, by row, the conjugate reversal of the other. E.g., 
row 4 of A125106 is 4 31 32 211 33 221 222 1111. The conjugates of 
these are 1111 211 221 31 222 32 33 4, which is row 4 of A242628 with 
the partitions in reverse order.

Curiously, this is exactly the relationship between our two primary 
enumerations of partitions, A036036 (or A036037) and A080577.

Franklin T. Adams-Watters

-----Original Message-----
From: franktaw <franktaw at netscape.net>
To: seqfan <seqfan at list.seqfan.eu>
Sent: Mon, May 19, 2014 1:13 pm
Subject: [seqfan] Re: Clarifying A112531


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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