$($b$)$ The sequence $(b_n{)}_{n}0$ with recursive definition $b_n=5b_{n-1}-6b_{n-2}$;$b_0=1,b_1=4.$

$($The sequence starts $1,4,14,46,146,$dots.$)$

A$.a{n}^2+bn+c$

B$.a{n}^3+b{n}^2+cn+d$

C$.a{3}^n+b(-1{)}^n$

D$.a{2}^n+b{3}^n$

Briefly explain: