8. There are three segments of length $2^{n}(n=0,1, \cdots, 1009)$ each, then the number of non-congruent triangles that can be formed with these 3030 segments is $\qquad$
(Answer with a number)
Answer: 510555
Explanation: (1) If $0 \leq i2^{j}, 2^{j}+2^{j}>2^{i}$, then $2^{i}, 2^{j}, 2^{j}$ must form a triangle;
(4) If $0 \leq k \leq 1009$, then $2^{k}, 2^{k}, 2^{k}$ must form an equilateral triangle.
Combining (1), (2), (3), and (4), we know that the only triangles that can be formed are $2^{i}, 2^{j}, 2^{j} (i<j)$ or equilateral triangles, totaling $C_{1010}^{2}+1010=510555$.