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_{k=1}^{28} a_{k} is divided by 1000.