Coding Challenge

Write a program that will determine the nth value of a recursively defined sequence as follows: n₁ = 1, n₂ = 2, n₃ = 3, but n_k+3 = n_k+2 + n_k+1 + n_k (mod 10,000) for each k>3. That is we take the sum and divide by 10,000 and take the remainder as the n_k+3.

You can write your code in any language. Just for fun. I'll take my hive rewards for this post, which might be as much as $1 and that will be the prize. I've already written one.
n₄=6
n₅=11
n₃₀=2016
n₅₀₀₀₀=504
n_1,000,000=9712
n_{1,000,000,000}=3184

What would be the value of n_{2020202020202020}?