# Counting lattice points.

• August 13th 2009, 12:50 PM
Vicky1997
Counting lattice points.
Let n be a positive integer, and R be the region defined by the simultaneous conditions x-y< n , x+y < n and x > 0. In terms of n
how many lattice points are contained in R?

If I didn't misunderstand the question I got 0 points for n=1 , 1 for n=2, 4 for n=3, 9 for n=4 . 16 for n=5.

How do I write this in terms of n?

Vicky.
• August 13th 2009, 02:20 PM
Matt Westwood
How about: $\left({n-1}\right)^2$?

Should be straightforward to prove it.
• August 13th 2009, 02:24 PM
Vicky1997
Thank You!!!!!!(Rofl)