The sequence you provided appears to be the sequence of perfect squares. Let's analyze it step by step:

• $1^2 = 1$
• $2^2 = 4$
• $3^2 = 9$
• $4^2 = 16$

Following this pattern, the next numbers in the sequence are:

• $5^2 = 25$
• $6^2 = 36$
• $7^2 = 49$
• $8^2 = 64$

So the sequence is: $1, 4, 9, 16, 25, 36, 49, 64$.

Would you like any details or have any questions? Here are some related questions:

1. What is the general formula for the $n$-th term in this sequence?
2. How can you prove that the sequence is made up of perfect squares?
3. What is the sum of the first $n$ perfect squares?
4. Can you find the difference between consecutive terms in this sequence?
5. What is the 10th term in this sequence?
6. How do perfect squares relate to areas of squares?
7. How does this sequence grow as $n$ increases?
8. How can you represent this sequence graphically?

Tip: For any integer $n$, $n^2$ is the square of $n$, and this sequence is generated by squaring successive integers.