How to continue this sequence from 64 combinations of Six Equal Parts, to 128 Combinations for Seven Equal Parts

Hi, 

I have a sequence that I need to continue. it is for my music rhythm course but involves an arithmetic sequence I believe and I'm getting quite confused. 

The image on the left is the official sequence. If you look at five equal parts, the total combination of the lines comes up with 32 Combinations. 

Now if you look at the Six equal parts, you see 64 Combinations. 

My task is to create the Seven equal parts, so adding a 7 to the sequence. I should, in the end, have 128 combinations. 

You have a starting of 1 dot, all the way up to 6 dots, and have to come up with all the combinations and variations with x amount of dots. 

My method is to eliminate from right to left with one dot. 

1 2 3 4 5 6 .
1 2 3 4 5 . 7 
1 2 3 4 . 6 7 
1 2 3 . 5 6 7 

and then when I start with the dots from right to left, and focus on eliminating one number specifically. 

2 Dots eliminating 7
1 2 3 4 5 . . 
1 2 3 4 . 6 .
1 2 3 . 5 6 . 
1 2 . 4 5 6 . 

And then I will do the same with 2 dots eliminating 6 and so on until I have done all the eliminations possible, 

My issue comes, when I get to the end and have to start eliminating from 3 down to 1, I don't know whether I am doing something wrong. 

If there is a flaw in my process please let me know I am happy to be put on the correct path as this has been a process of frustration and roadblocks!

Thank you  

  • I think the offered bounty is a bit low for the time it may take someone to answer this question.

  • Thanks, I didn't even factor in the deadline. Will change

  • Could you clarify what you mean by "equal parts"? Your question is a little vague.

  • It is in the picture, it's just the name of the sequence. for example, in the picture, you see five equal parts in the same sequence but from numbers 1 2 3 4 5 and then six equal parts in the same sequence but with numbers 1 2 3 4 5 6. My task is to make Seven Equal Parts with the same sequence but with numbers 1 2 3 4 5 6 7.

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  • Hi, Thank you for your response, this method is in line with the sequence from what I understand. Where the issue lies for me is, when I have to create +2 dots +3 +4 dots for example. to get to that magical 128, so in the image you see the section Six Equal Parts the first line is 6 numbers 6 dots then: 1 dot 5 numbers then flipped 2 dots 4 numbers etc 1 dot 6 numbers mirror 6 dots 1 number 2 dots 5 numbers / 5 dots 2 numbers 3 dots 4 numbers / 4 dots 3 numbers

  • im just struggling to know how many I would do in each category as I add more dots, sorry to be confusing

  • Just write two copies of all combinations for 123456. Add 7 to the end of the first copy and add dot to the end of the second one. Then you will have 64*2=128 combinations for 1234567.

  • Amazing, thank you Phillip/

  • You're welcome. I am glad I was able to help.

The answer is accepted.