Q3 (4 points)
How many solutions (in non-negative integers) are there to the equation
$$t_1 + t_2 + \dots + t_k + s_1 + s_2 + \dots + s_k = n,$$
where $$t_i \in \{0, 3\}$$ and $$s_i \equiv 1 \pmod 3$$ for $$i = 1, \dots, k$$? Check your answer by listing all solutions for $$n = 11$$ and $$k = 2$$ (For instance, $$(t_1, t_2, s_1, s_2) = (0, 3, 1, 7)$$ is a solution).
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