My recursive algorithm, statified into two methods:

My recursive algorithm, stratified into two methods:

Consider the infinite sequence of numbers An|n>0 = (1,1,3,4,8,11,...) defined recursively as follows.
A1 = A2 = 1.
An = Bn−1 + An−2, if n > 2.
B1 = B2 = 2.
Bn = An−1 + Bn−2, if n > 2.

Consider the infinite sequence of numbers An|n>0 = (1,1,3,4,8,11,...) defined recursively as follows.

$$ A_n = \left\{\begin{aligned} &1 && n = 1,2\\ &B_{n-1}+A_{n-2} && n > 2 \end{aligned} \right. \\ B_n = \left\{\begin{aligned} &2 && n = 1,2\\ &A_{n-1}+B_{n-2} && n > 2 \end{aligned} \right. $$