A series of numbers: Help needed

[tulamide]

I hope somebody will be able to help with this. There's a series of numbers. The series will have a minimum of 2 layers, but can go as high as imaginable. I evaluated the progression of the first five evolutions.

For 2 layers: 0, 1
For 3 layers: 0, 2, 3
For 4 layers: 0, 4, 6, 7
For 5 layers: 0, 16, 24, 28, 30
For 6 layers: 0, 32, 48, 56, 60, 62

I know it is somehow a reversed base 2 exponential. The differences from layer to layer can be expressed as 2^x. If I only write down those differences as x, it looks like this:

0
1, 0
2, 1, 0
4, 3, 2, 1
5, 4, 3, 2, 1

Damn, it was so close! But it still isn't a linear progressing series. Look at the break between 4 and 5 layers. For 4 layers it is 2, 1, 0 and not 3, 2, 1. But then again they both progress linear towards their other neighbours...

Is there anybody out there who could help me getting to the formula behind this? I need it to calculate any of the numbers for any amount of layers (Like 32 for the second layer if there are six in total, but 2 for the second layer if there are only three in total). Probably I don't see the tree for the woods.

[Youlean]

Are you sure that layer 5 is not 0, 8, 4, 2, 1, and layer 6: 0, 16, 24, 28, 30, 31?

[djbrynte]

what u doing?

[tulamide]

Are you sure that layer 5 is not 0, 8, 4, 2, 1, and layer 6: 0, 16, 24, 28, 30, 31?

Yes, unfortunately It is exactly as I wrote it down. That's why I have an issue.

@djbrynte could you please stop pushing your own posts every few minutes to be shown on top, and give others a chance to be noticed, too? Thanks.

[djbrynte]

I asked what r u trying to do now? Is it something unison related?

[Youlean]

Hm, can you write down more layers? It is hard to assume math behind it if the has change occured only once. If there is another change it will be much easier to find solution...

[martinvicanek]

If you write it down in binary representation, the structure becomes evident, including the irregularity in the transition from layer 4 to layer 5 (a factor 2):

Code: Select all

layer 2: 0 1      
layer 3: 0 10     11
layer 4: 0 100    110    111      
layer 5: 0 10000  11000  11100  11110   
layer 6: 0 100000 110000 111000 111100 111110

[tulamide]

I know, Martin. That's what's making me crazy. But the numbers are correct!

For 7 layers: 0, 64, 96, 112, 120, 124, 126
For 8 layers: 0, 128, 192, 224, 240, 248, 252, 254

And here's a rough sketch of what I'm trying to do:

tree-scheme.png (8.71 KiB) Viewed 13613 times

Green is just an example. I need it for every first circle per row. Now, the only constant in this is that the last row will always have the circles directly aligning. For that graphic x is 4 for row 1, 6 for row 3 and 7 for row 4. I've listed x for trees up to 8 layers now, and there is this break between 4 and 5

[martinvicanek]

Are you sure that you're not mixing up r and d (= 2r)?

[stw]

if i understand your sketch correctly
row 5 should read: 0,8,12,14,15
row 6 should read: 0,16,24,28,30,31

which would be easy to solve...?