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.