/sci/ - Science & Math

Say you have three variables, a,b,c
These variables can only have positive integer values (1 or bigger), and they have the constraints: 0 < a < b < (c-a), b ≠ 2a
Since c is bigger than b and a, you can sort the possible combinations by c, the biggest variable

like this:
a - b - c
1 - 3 - 5
1 - 3 - 6
2 - 3 - 6
1 - 4 - 6
1 - 3 - 7
2 - 3 - 7
1 - 4 - 7
1 - 5 - 7
1 - 3 - 8
etc

what is the growth rate of c? is there a function where x represents the xth place in the list, and y is the value of c?
all I know is that it's the inverse of a polynomial, does it have to be approximated, or can I figure out an exact formula by looking at the constraints?

I'd like to add that if the constraints were just a < b < c, then the function would be the inverse of the triangular number function, x(x+1)/2
so it's something similar, right? does b ≠ 2a fuck it up? what if you ignore that constraint and just focus on the 0 < a < b < (c-a) part?

Say you have three variables, a,b,c
These variables can only have positive integer values (1 or bigger), and they have the constraints: 0 < a < b < (c-a), b ≠ 2a
Since c is bigger than b and a, you can sort the possible combinations by c, the biggest variable

like this:
a - b - c
1 - 3 - 5
1 - 3 - 6
2 - 3 - 6
1 - 4 - 6
1 - 3 - 7
2 - 3 - 7
1 - 4 - 7
1 - 5 - 7
1 - 3 - 8
etc

what is the growth rate of c? is there a function where x represents the xth place in the list, and y is the value of c?
all I know is that it's the inverse of a polynomial, does it have to be approximated, or can I figure out an exact formula by looking at the constraints?