Sums of Ceiling Functions Solve Nested Recursions

Rafal Drabek, Abraham Isgur, Vitaly Kuznetsov +1

It is known that, for given integers s \geq 0 and j > 0, the nested recursion R(n) = R(n - s - R(n - j)) + R(n - 2j - s - R(n - 3j)) has a closed form solution for which a combinat…