How many ways can a number be written as a sum of two non negative integers?
For example there is $4$ way for $7$. $ 7=0+7=1+6=2+5=3+4$
I think there is $[ \frac{N}{2}]+1$ way for number$N$. Is it true?
2026-03-29 14:07:24.1774793244
How many ways can a number be written as a sum of two non negative integers?
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If you consider 3+4 and 4+3 as two different ways then yes it will be N+1. Think of it as placing a partition in a row of N objects you can place it right in the beginning, right at the end and any of the N-1 locations. However if 3+4 and 4+3 are considered same then we have only 4 ways of writing 7 as sum of two numbers. In this case the answer will be ceil((N+1)/2) where ceil(x) is smallest integer greater is Han or equal to x.