[seqfan] Re: Regarding A122172 - A proper definition is needed for this sequence
franktaw at netscape.net
franktaw at netscape.net
Thu Aug 4 02:28:22 CEST 2011
This can be regarded as a tabf sequence in two different ways. One has
one row per rectangular array, so nth row has (n+1)*Part(n) elements.
The other way is with one row of a table counting as a row of the
sequence. Thus this produces row lengths of 1, 2, 3,3, 4,4,4,
5,5,5,5,5, ....
Franklin T. Adams-Watters
-----Original Message-----
From: David Scambler <dscambler at bmm.com>
Part of the problem with presenting this sequence is that it is an
infinite
sequence of rectangular arrays, not of integers.
The j'th array in the triangle has j+1 columns and partitions(j) rows.
Each row of the j'th section corresponds to a partition of j and
answers the
following question:
How many ways may 0<=k<=j indistinguishable balls be dropped into a set
of urns
whose maximum capacities
are determined by the parts of a partition of j?
e.g. j = 3
Urns k= 0 1 2 3
======== =======
(3) 1 1 1 1
(2)(1) 1 2 2 1
(1)(1)(1) 1 3 3 1
dave
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