Function to get various numbers based on two inputs

Question

I have some "centering" rules that involve a calculation using a count and index. Both count and index are between 1 and 5. The goal is to center a set of items around a given starting point ( in this case -12 ).

The returned value is determined as follows, by looking up the count and then the index:

{
    count: {
        index: value
    }
}

If I represent all possible values as a dictionary (in python) it looks like this:

{
    1: {
        5: -12
    },
    2: {
        5: -21,
        4: -3
    },
    3: {
        5: -30,
        4: -12,
        3: 6
    },
    4: {
        5: -39,
        4: -21,
        3: -3,
        2: 15
    },
    5: {
        5: -48,
        4: -30,
        3: -12,
        2: 6,
        1: 24
    }
}

What kind of formula can express these relationships? I can see a clear difference of 18 between each value in a given series, but I'm having trouble with the odd/even difference.

Answer 1

Since when count is increased, the value gets reduced by 9,

and when index is increased, the value gets reduced by 18, we obtain a function of the form:

$$f(count, index) = c - 9^*count - 18^*index$$

where $c$ is to be determined. Substituting $count=index=3$ (or any other value):

$$f(3,3) = c-81=6 \implies c=87$$

Hence your function would be:

$$f(count,index) = 87-9^*count-18^*index$$