Mr. Me obviously knows it

$\text{22, 35, 48, 61, 74, 87, 100, 113,} \dots$

Above is a recursive sequence such that $T_0=22$ and $T_1=35$ . And the general term $T_n$ for $n \ge 2$ is given as $T_n=2T_{n-1}-T_{n-2}$ .

Write a recursive function using the above definition to find the $T_n$ for any integer $n \ge 0$ .

What is the $number$ of function calls for getting the $22^{nd}$ term $\left( T_{22} \right)$ ?

Hint: The $number$ contains $5$ digits and the digits are $1$ , $2$ , $3$ , $4$ and $5$ .