Question

I have a list of items, that all need to be linked.

To determine the count for 4 linked items (in terms of established links)

you start at 3

3 + 2 + 1 which yields 6

Every preceding integer value.

Another example To get the link count for 5 items you do

4+3+2+1 yields 10

Is there a term for this? It is similar to factorials in the sense that every preceding integer value is used, but different in that the operator is addition in stead of multiplication.

Thanks in advance.

Answer 1

They are called triangular numbers.

http://en.wikipedia.org/wiki/Triangular_number

http://www.research.att.com/~njas/sequences/A000217

Answer 2

The comment by Helge is correct. They even have a name - the Triangular numbers.

Slightly more interesting is the same idea but for $\frac{1}{i}$ and addition gives you the harmonic numbers.