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 $$\sum^{28}_{k=1} a_k$$ is divided by 1000.

(第二十四届AIME2 2006 第11题)