[seqfan] Partitions and Dice

[Toby]

----- Original Message -----
Subject: Partitions and Dice
Date: Fri, 20 Feb 2009 19:06:13 -0500
From: franktaw at netscape.net
....
Second, the comment from Toby Gottfried in A102422 is fine, but the one
in A102420 is not correct.  This is 5 "5-sided" dice, not 4 6-sided dice.

Franklin T. Adams-Watters
----------------------------------------------------------------

It's both.    Same numbers work for two different criteria.


A102420      Number of partitions of n with exactly k = 5 parts and each part p <= 5

New:  exactly 4 parts and 1 <= p <= 6  ... regular dice  (and different offset by 1 in 
sequence)

Example: a(10) = 6.

5 dice, total 10 (max value 5)
5,2,1,1,1
4,3,1,1,1
4,2,2,1,1
3,3,2,1,1
3,2,2,2,1
2,2,2,2,2
------------ 6 partitions

4 dice, total 9 (max value 6)
6,1,1,1
5,2,1,1
4,3,1,1
4,2,2,1
3,3,2,1
3,2,2,2
------------- 6 partitions