We think that the bottom line has to add up to an odd number.
We also found out that there has to be a one in in the bottom row.
The middle line can't have a one in it.
The second to bottom row will equal to 11, 12, 13.
On the bottom row a number will always be repeated twice or three times.
There are only 4 pairs of numbers that can be used in the second row.
15 15 15 15 15
8 7 8 7 7 8 4 11 10 5
4 4 3 6 2 5 4 3 5 2 2 9 8 2 3
2 2 2 1 5 1 1 4 3 1 2 3 1 1 1 8 7 1 1 2
15 15 15
5 10 6 9 6 9
2 3 7 2 4 5 3 3 6
1 1 2 5 1 1 3 2 2 1 2 4
Extension:
We combined your idea and we did our own version using decimal points
15
9 6
6 3 3
4 2 1 2
2.5 1.5 .5 .5 1.5
1.25 1.25 .25 .25 .25 1.25
.125 1.125 .125 .125 .125 .125 1.125