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

[William Rex Marshall]

From: "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 think your hand-figuring contains errors. First term should be 0. 9th term should be 8:

{1,1,1,1,1,1,1,1,1}
{3,3,3}
{1,3,5}
{2,3,4}
{1,8}
{2,7}
{3,6}
{4,5}

The correct sequence should be http://www.research.att.com/~njas/sequences/A049990.