Determine the # of ways to get from (0,0) to (2,2) ..

I found it is 6 because of

(2,0) = 1

(2,1) = 3

(2,2) = 6

(2,3) = 10

(2,4) = 15

(2,5) = 21

(2,6) = 28

etc..

so who can give me a formula to explain this relationship for a general thing?

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- Dec 3rd 2008, 07:09 PMIdeasmanFormula
Determine the # of ways to get from (0,0) to (2,2) ..

I found it is 6 because of

(2,0) = 1

(2,1) = 3

(2,2) = 6

(2,3) = 10

(2,4) = 15

(2,5) = 21

(2,6) = 28

etc..

so who can give me a formula to explain this relationship for a general thing? - Dec 3rd 2008, 07:11 PMvincisonfire
It seems to be $\displaystyle *\sum_{n=1}^{n}i=\frac{n(n+1)}{2} $ But the thing is like delayed by 1. So $\displaystyle \sum_{n=1}^{n}i+1=\frac{(n+1)(n+2)}{2} $