Partitions of n into distinct parts >=10

[Edwin Clark]

On Wed, 7 Jan 2004 all at abouthugo.de wrote:

> 
> SeqFans,
> 
> there are two (similar?) sequences, both by Clark Kimberling:
> 
> %S A025155
> 0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,6,7,7,9,9,11,12,
> %T A025155 14,15,18,19,22,24,27,29,33,36,40,44,49,54,60,66,73
> %N A025155 Partitions of n into distinct parts >= 10.

It should be "The number of partitions of n into distinct parts >= 10."

Say, n = 11. Then there is one and only one partition of n into distinct
parts each of which is >= 10. Namely 11 = 11.

On the other hand there is no way to partition 11 into n distinct parts if
one of the least parts is 10. Since 11 = 10 + x where x >= 10 has no
solutions.
> 
> and
> 
> %S A026831 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,
> %T A026831
> 1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,10,11,13,14,16,18,20,22,25,27,
> %U A026831 30,33,36
> %N A026831 Partitions of n into distinct parts, the least being 10.
> 
> Could anybody explain the differences and provide more concise
> titles and definitions?
> 
> Hugo Pfoertner
>