Any Mathematicians Out There?

Does anyone know if there's a name for a series of sums made of the maximum integer values of pairs of addends? Or to put it another way, the difference between the addends is always 0 or 1. For example:

1 = 1 + 0
2 = 1 + 1
3 = 2 + 1
4 = 2 + 2
5 = 3 + 2
6 = 3 + 3
7 = 4 + 3
8 = 4 + 4
9 = 5 + 4

As opposed to a series like:

1 = 0 + 1
2 = 1 + 1
3 = 2 + 1
4 = 3 + 1
5 = 4 + 1
6 = 5 + 1
7 = 6 + 1
8 = 7 + 1
9 = 8 + 1

Well?