Here are 20 lucky 7-number sequences based on the new constraints:

1. [14, 23, 4, 17, 20, 3, 27]
2. [17, 29, 3, 28, 19, 2, 27]
3. [25, 2, 15, 16, 28, 7, 1]
4. [22, 12, 3, 16, 19, 1, 20]
5. [19, 27, 12, 21, 15, 17, 16]
6. [32, 7, 28, 12, 4, 23, 17]
7. [16, 30, 31, 9, 13, 17, 20]
8. [11, 25, 7, 23, 4, 24, 20]
9. [34, 2, 3, 25, 21, 1, 19]
10. [11, 24, 19, 3, 8, 15, 12]
11. [19, 2, 7, 14, 29, 23, 28]
12. [34, 5, 12, 32, 16, 23, 24]
13. [31, 26, 18, 30, 11, 6, 23]
14. [24, 10, 3, 8, 23, 18, 5]
15. [29, 1, 4, 17, 26, 30, 33]
16. [14, 24, 32, 1, 30, 22, 21]
17. [10, 30, 13, 26, 9, 1, 4]
18. [3, 4, 1, 32, 2, 22, 35]
19. [19, 6, 3, 11, 31, 21, 4]
20. [28, 35, 12, 22, 1, 30, 20]

Would you like more details or have any questions?

Here are 5 more questions you might ask:

1. Can you show the frequency of each number in these sequences?
2. How are the required numbers distributed in the sequences?
3. Can you generate similar sequences with different sum constraints?
4. What is the maximum and minimum sum of these sequences?
5. Can you verify if each number from 1 to 35 appears at least once?

Tip: When generating random sequences, always double-check your constraints to ensure they align with your requirements, especially when multiple conditions need to be met.