CURIOUS NUMBERS

The number `48` has this peculiarity, that if you add `1` to it the result is a square number (`49`, the square of `7`), and if you add `1` to its half, you also get a square number (`25`, the square of `5`). Now, there is no limit to the numbers that have this peculiarity, and it is an interesting puzzle to find three more of them—the smallest possible numbers. What are they?