# Inspired by shubhendra Singh

A sequence is defined as follows $$a_1=a_2=a_3=1$$ , and, for all positive integers $$n$$ , $$a_{n+3}=a_{n+2}+a_{n+1}+a_n$$ . Given that $$a_{28}=6090307, a_{29}=11201821$$, and $$a_{30}=20603361$$, find the remainder when $$\displaystyle\sum^{28}_{k=1} a_k$$ is divided by 1000.

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