Create equation with two numbers [closed]

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I need a formula to define the relation between the length of a list in this example (2) and the number of elements which is here (4) to calculate the number of combinations which is (10).

Example:

(1,1)   
(1,2)  
(1,3)  
(1,4)  
(2,2)  
(2,3)  
(2,4)  
(3,3)  
(3,4)  
(4,4)

Answer 1

The equation should be,

f(n) = n*(n+1) / 2, f(n) is length

f(4) = 4 * 5 / 2 = 10

Answer 2

Here's how you derive the formula.

There are 4 entries with one as the first component: (1,1), (1,2), (1,3), (1,4), 3 entries with two in the first component, 2 with three and 1 with four.

That's 1 + 2 + 3 + 4. If you have 5 elements, it's 1 + 2 + 3 + 5, if you have 2 elements, it's 1 + 2.

It's clear we need a formula to evaluate 1 + 2 + 3 + ... + n

By rearranging the sum, we get terms that all evaluate to n + 1, since we always grouped two numbers, we have n/2 such terms. Hence n/2 * (n + 1)