Leetcode 1269. Number of Ways to Stay in the Same Place After Some Steps

Count the number of sequences of left/right/stay moves on a 1D array of length arrLen starting at index 0 that return to index 0 after exactly steps moves (answer modulo 1e9+7). This is a DP/counting problem over steps and positions — with steps ≤ 500 you can limit the positions considered to O(min(arrLen, steps)) to compute ways efficiently.