The sequence follows a pattern where each number is double the previous number and then adds
1: \( 2 \times 2 + 1 = 5 \),
\( 5 \times 2 + 1 = 11 \),
\( 11 \times 2 + 1 = 23 \),
\( 23 \times 2 + 1 = 47 \).
The next term is \( 47 \times 2 + 1 = 95 \).
Find $P_1 + P_2 + \dots + P_{10}$ if $P_k$ is the perimeter of a square having side length $k$.