I am looking for the image of the following function:
f(a,b) = ((a+1) * (a+2b)) / 2
a and b are natural numbers and the image is also contained in natural numbers.
For the solution of the problem, I plugged in even and/or odd numbers for a and b and tried to see a pattern. But, I could not see a distinct pattern. When the numbers are small, it seems that we can get almost as many odd numbers as even numbers as the output, but when a and b get larger and have lots of zeros, even results seemed to come out more.
I would really appreciate, if you could give your thoughts on this...