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

Andrew Plewe aplewe at sbcglobal.net
Mon Feb 5 07:51:58 CET 2007

```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-

```