[seqfan] A095814

David Newman davidsnewman at gmail.com
Fri Jun 7 07:37:04 CEST 2013


I'm still having problems with this sequence, but this time the problem is
not in the nature of a typographical error.

We have four sources of knowledge about this sequence, the numbers in the
sequence itself, the comment, the formula, and the title.  The only ones
which seem to agree are the sequence and the formula.

The title does not seem clear to me.  It is:  "Number of nonisomorphic
partitions of  n on the Ferres graph".  I take this to mean "the number of
unrestricted partitions of n up to conjugation," where conjugation is the
familiar operation of flipping the Ferrers graph so that rows become
columns and columns become rows"

If this is the correct interpretation of the title, then a(n) should be the
number of self-conjugate partitions of n, plus one half the number of
partitions of n which are not self-conjugate.  To give an example:  The
number of unrestricted partitions of 10 is 42.  There are 2 self-conjugate
partitions :52111 and 4321.  So a(10) should be (42-2)/2  +2=22.  But
A095814(10)=21.

Let's try calculating a(10) using the comment.  The comment reads:
"partitions of n into at most ceil(n/2) parts and with at least one part
greater than or equal to n-floor(n/2)"  For n=10 this becomes "partitions
of 10 into at most 5 parts and with at least one part greater than or equal
to 5."

Here is a list of such partitions:

1.     10
2.      91
3.      82
4.      811
5.      73
6.      721
7.      7111
8.      64
9.      631
10.     622
11.     6211
12.     61111
13.     55
14.     541
15.     532
16.     5311
17.     5221
18.     52111

This seems to give a(10)=18.


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