more on A119028 and Re: Identical-digit blocks in decimal representation of partition numbers

[Joseph Biberstine]

	You're too kind.  I wish I could take credit for the sequence, but I
really just followed the breadcrumbs in response to Tanya Khovanova.
	Your interest inspires me to share a message from a dialogue I had with
Robert G. Wilson v last month.  This natural generalization of the
sequence seems to have a beautiful graphical interpretation.
Unfortunately the awkward code I have won't allow me to generate more
terms efficiently, so we only see what I suppose is the tip of a most
pleasant iceberg.

-JRB

Jonathan Post wrote:
He recently gave us the rather pretty:
> A119028 <http://www.research.att.com/%7Enjas/sequences/A119028> 	
> 	Numbers that have 3 different *partitions* into 3 parts with the same
product.

-------- Original Message --------
Subject: Re: Proposed joint submittal.
Date: Fri, 28 Jul 2006 01:54:00 -0400
From: Joseph Biberstine <jrbibers at indiana.edu>
To: rgwv at rgwv.com

tanya[n_, p_] := Max[Length /@ Split[Sort[Times @@@ Partition[Last /@
Flatten[FindInstance[a + b + c == n && a >= b >= c > 0, {a, b, c},
Integers, PartitionsP[n]]], p]]]];
Table[tanya[k + p, p], {p, 2, 8}, {k, 2, 34}] //MatrixForm

	Which comes out looking like this (hopefully your mail client can handle):

1 1 2 2 1 2 4 2 3 3 2 3 4 4 3 3 3 4 4 4 4 4 4 4 4 2 4 4 4 4 5 4 4
1 1 1 1 1 1 1 1 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 1 1 1 2 1 1 2 2 1 2 1 1 1 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 1 2 2 2
1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 2 1 2 1 1 2 2 2 2 1 1 1 2 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

	Pretty, huh?  Looks like some neat chaotic curtain effect.  Attached is
a graphical interpretation.

JRB
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