I have a formula F that takes an ordered pair (a,b) of positive integer variables and outputs an unique positive integer c for each pair. Then I was working around with the formula and noticed that where i is added to a and subtracted from b to get (a',b') and in every case F(a',b') equals c + i . Then I thought that since i is both added and subtracted, the sum of the pair does not change with the value i and you can make i equal a+b-c so that F(a',b') = a' + b'.(adsbygoogle = window.adsbygoogle || []).push({});

This gave the following ordered pairs for each integer:

.

.

.

-4 (6,-10)

-3 (3,-6)

-2 (1,-3)

-1 (0,-1)

0 (0, 0)

1 (1, 0)

2 (3, -1)

3 (6, -3)

Here a and b are the positive and negative triangular numbers. The ordered pairs form a curve. In between points could be filled in by making a and b real instead of integers. Now if i is added to each a and subtracted from each b the shape of the curve does not change.

What is the formula for such a curve that passes through the above points? Please help me.

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# What is the formula for this curve?

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