Help extending sequence: Partition of n into constant-spaced integers

[Andrew Plewe]

I propose the following sequence: the number of partitions of n into 
constant-spaced integers. For example, 14 has (as I count them) 10 
partitions:

7.6.5.4..3..2..1
7.8.9.10.11.12.13

2 2 2 2 2 2 2

1 1 1 1 1 1 1 1 1 1 1 1 1 1

5
4
3
2

I'm currently figuring out the sequence by hand, if anyone wants to 
extend it or write a program to generate it then that'd be most 
appreciated. So far I've worked out the first 15 terms:

1, 1, 2, 3, 3, 6, 4, 6, 4, 7, 6, 12, 7, 10, 15

I will continue to work out the others as well. Is it always true that 
the number of partitions of n will be less than or equal to n? Also, 
looking at these partitions seem to suggest that the number of ways to 
express an integer as the difference of two figurate numbers is always 
less than the number of partitions into constant spaced integers. The 
number of those representations would be another sequence. Thanks!

    -Andrew Plewe-