2026 AIME II Problem 14

For integers a and b, let a \circ b = a - b if a is odd and b is even, and a+b otherwise. Find the number of sequences a_1, a_2, a_3, \ldots, a_n of positive integers such thata_1 + a_2 + a_3 + \cdots + a_n = 12 \quad \text{and} \quad a_1 \circ a_2 \circ a_3 \circ \cdots \circ a_n = 0where the operations are performed from left to right; that is, a_1 \circ a_2 \circ a_3 means (a_1 \circ a_2) \circ a_3.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.