1. **Stating the problem:** We have a sequence where the number of tiles used in each entry forms a pattern: Entry 1 uses 1 tile, Entry 2 uses 4 tiles, Entry 3 uses 9 tiles, Entry 4 uses 16 tiles, and so on. 2. **Identifying the pattern:** Notice that the number of tiles corresponds to perfect squares: $1 = 1^2$, $4 = 2^2$, $9 = 3^2$, $16 = 4^2$. 3. **Formula used:** The number of tiles $T$ in entry number $E$ is given by the formula: $$T = E^2$$ 4. **Explanation:** This means for any entry number $E$, the number of tiles used is the square of $E$. For example, the 5th entry will have $5^2 = 25$ tiles. 5. **Summary:** The sequence of tiles is the sequence of perfect squares, and the formula $T = E^2$ describes the number of tiles used at entry $E$.