[seqfan] Re: a sequence to check

[franktaw at netscape.net]

Also working basically by hand, but cross-checking A000219 and A098859, 
I get a(6) = 32, not 31. I also get a(7) = 68, so the sequence starting 
at n=0 is:

1,1,3,4,11,20,32,68

For n=6, by partition: [6]->1, [3^2]->2, [4,1^2]->3, [2^3]->3, 
[3,1^3]->5, [2,1^4]->7, [1^6]->11.

Franklin T. Adams-Watters

-----Original Message-----
From: David Newman <davidsnewman at gmail.com>

I'd like someone to check (and extend) the following.

What is the number of plane partitions each of whose summands is used a
different number of times.

As an example for n=3 there are 4 such partitions

3

111

11
1

and

1
1
1.

The plane partitions

21 and

2
1

do not appear on the list because each of the summands "2" and "1" is 
used
the same number of times.


The numbers that I've gotten, for n=1 until n=6, by hand calculations 
are:
1,3,4,11,20, and 31