>>>Sum=(N^3)/6+(N^2)/2+N/3
>>>If this is right, I will send you bill ::)
>>
>>Ladies and gents, we have a winner! That is, converting, the same as my solution of Gifts = n * (n+1) * (n+2) / 6. Congratulations, Edward!
>
>OK, Bruce, you've done it again. It's like a song I can't stop singing in my head.
>
>if my Algebra II memory serves me right, the proper way to write this formula is:
>

>n * (n+1) * (n+2)
>-----------------
>    (1*2*3)
>

>what kind of problem is this?

It's combinatorics, at least that's how I solved it:

 (n+2)          (n+2)!         (n+2)(n+1)n
C       = ----------------- = ------------------,
 (n-1)   (n-1)! (n+2-(n-1)!         3!

after canceling like terms of factorials.