$a_n = a_{n-1} + a_{n-2}$ with $a_1 = 1, a_2 = 2$

$a_n = 2a_{n-1} + a_{n-2}$ with $a_1 = 1, a_2 = 3$

$a_n = a_{n-1} + 2a_{n-2}$ with $a_1 = 1, a_2 = 3$

$a_n = a_{n-1} + a_{n-2} + a_{n-3}$ with $a_1 = 1, a_2 = 2, a_3 = 4$