<Li> in the quadrant x ≤ 0, y ≥ 0 (\ displaystyle x \ leq 0, y \ geq 0) the function is alternatingly very large positive and negative on the parallelograms with vertices </Li> <Dl> <Dd> (− n, m + 1), (− n, m), (− n − 1, m − 1), (− n − 1, m) (\ displaystyle (- n, m + 1), (- n, m), (- n - 1, m - 1), (- n - 1, m)) </Dd> </Dl> <Dd> (− n, m + 1), (− n, m), (− n − 1, m − 1), (− n − 1, m) (\ displaystyle (- n, m + 1), (- n, m), (- n - 1, m - 1), (- n - 1, m)) </Dd> <Ul> <Li> in the octant 0> x> y (\ displaystyle 0> x> y) the behavior is again alternatingly very large positive and negative, but on a square grid . </Li> <Li> in the octant − 1> y> x + 1 (\ displaystyle - 1> y> x + 1) it is close to zero, except for near the singularities . </Li> </Ul>

Sum of k choose m up to n