SMO 2008 Problem 3

let n,m be positive integers st $m>n\geq 5$ with m depending on n. consider the sequence $a_1,a_2,...a_m$ where $a_i=i$ for $i=1,...,n$ $a_{n+j}=a_{3j}+a_{3j-1}+a_{3j-2}$ for $j=1,..,m-n$ with $m-3(m-n)=$ 1 or 2, ie $a_m=a_{m-k}+a_{m-k-1}+a_{m-k-2}$ where k=1 or 2 (Thus if $n=5$ , the sequence is 1,2,3,4,5,6,15 and if $n=8$ , the sequence is 1,2,3,4,5,6,7,8,6,15,21) Find $S=a_1+...+a_m$ if (i) $n=2007$ (ii) $n=2008$