1. **Problem statement:** We have a recurrence relation defined as $$a_n = a_{n-1} + a_{n-3}$$ for $$n \geq 3$$ with initial conditions $$a_0 = 1$$, $$a_1 = 1$$, and $$a_2 = 1$$. 2. **Goal:** Find the first several terms of the sequence and understand its behavior. 3. **Step-by-step calculation:** - For $$n=3$$: $$a_3 = a_2 + a_0 = 1 + 1 = 2$$ - For $$n=4$$: $$a_4 = a_3 + a_1 = 2 + 1 = 3$$ - For $$n=5$$: $$a_5 = a_4 + a_2 = 3 + 1 = 4$$ - For $$n=6$$: $$a_6 = a_5 + a_3 = 4 + 2 = 6$$ - For $$n=7$$: $$a_7 = a_6 + a_4 = 6 + 3 = 9$$ 4. **Explanation:** Each term is the sum of the previous term and the term three places before it. This creates a sequence that grows by combining recent and earlier values. 5. **Summary of terms:** $$a_0=1$$, $$a_1=1$$, $$a_2=1$$, $$a_3=2$$, $$a_4=3$$, $$a_5=4$$, $$a_6=6$$, $$a_7=9$$. This sequence can be further analyzed or used to find more terms as needed.