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

[Giovanni Resta]

Andrew Plewe wrote:
> 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: 
Actually, they are 11, since also {14} itself must be counted:
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 13},
{2, 2, 2, 2, 2, 2, 2}, {2, 3, 4, 5}, {2, 12}, {3, 11},
{4, 10}, {5, 9}, {6, 8}, {7, 7},{14}

The sequence you are considering it is already in the OEIS.
See  A049988
a(n)=number of arithmetic progressions of positive integers,
nondecreasing with sum n.

g.