$a_n = 2a_{n-1} + 1$ with $a_0 = 1$

$a_n = 2a_{n-1} - 1$ with $a_0 = 1$

$a_n = a_{n-1} + 2^{n+1}$ with $a_0 = 1$

$a_n = a_{n-1}^2 - 2$ with $a_0 = 1$