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In the coordinate plane, a lattice point is a point with integer coordinates. Suppose n is a positive integer. How many lattice points (x,y) are there such that (x,y) lies in the region defined by the inequalities 0<=x<=n, 0<=y<=n, and |x-y| <=1?

 May 12, 2023
 #1
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The region defined by the inequalities is a diamond with side length n+1. The number of lattice points in a square with side length n is n^2, so the number of lattice points in a diamond with side length n+1 is ((n+1)^2−n^2)/2​ = n^2 + n.

 May 12, 2023
 #2
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Its incorrect

Quakwise  May 12, 2023

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