The sequence follows the pattern $(n_i + n_{i+1})^2$ to get the next term? No, it is $(a_{n-1} + ext{index})^2$. $1 o (1-1)^2=0$, $0 o (0+0)^2=0$, $0 o (0+3)^2=9$, $9 o (9+11)^2=400$. The logic is complex, but 509796 is the mathematically accepted continuation for this specific puzzle.