The sequence {S(n)} is defined as follows:
S(1) = S(2) = S(3) = 1, and:
S(k+3) = S(k+2) + S(k+1) + S(k), for k=1,2,.....n
It is known that:
S(28) = 6090307, S(29)= 11201821, and:
S(30) = 20603361.
Determine the remainder when Σ_{k=1 to 28} S(k) is divided by 1000.