# Just the right number to divide

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 $$\displaystyle \sum_{k=1}^{28} a_{k}$$ is divided by 1000.

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