Hi Forum

I've found this Order of Differences problem, which I can't find information on.

This may be recurrent on sequences, maybe I got the name of it wrong.

Anyway

We are to find the sum of the first 7 terms in this sequences.

Code:

1
> 2
3 > 1
> 3
6 > 1
> 4
10 > 1
> 5
15

The solution says something about T(n) being of the second degree.

Then later it states

1=a+b+c

3=4a+2b+c

6=9a+3b+c

The 1, 3 and 6 part is related to the number of points in the triangle but what does the other part means?

This seems like a complex sequence at first.

Can someone help?

Thanks