Math Question: Pascal

Friend of Iac’s, I can’t quite figure it out but have some ideas. Thougt you guys could help.

In a formula, what is the relation between the number of the rows in pascals triangle and the number of odd numbers in that row?

(Iac) All I can figure is this pattern: If you count the first row (1) as 1 instead of as 0, the number of odds equals the row number every power of two (as in, the first (0th) row has 1, 2nd has two, 4th has four, etc.). Also, halfway between powers of two is the earlier number, or half the second one, and halfway between those is the earlier number/half of that. In example, between 8 and 16:
8 - 8
9 - 2
10-4
11-4
12-8
13-4
14-8
15-8
16-16
Or repeat that pattern and repeat again with double the numbers for the second half.

So I can do it sensibly in my head, but I can’t find a formula, and now I’m compelled to know. Can I get help or a hint, please?

This link should give you a lot of interesting information. There are some interesting formulas and properties of the sequence listed there.

Check out this link too.