[R] Double summation limits

[RON70]

Can anyone please explain me why it is not coming? I have done following :

> j=1
> i=0:j; sum( choose(i+j,i) )
[1] 3
> j=2
> i=0:j; sum( choose(i+j,i) )
[1] 10
> j=3
> i=0:j; sum( choose(i+j,i) )
[1] 35
> j=0:3; i=0:j; sum( choose(i+j,i) )
Warning message:
In 0:j : numerical expression has 4 elements: only the first used
[1] 4

Here if value of "j" is given independently it is ok. However as soon as "j"
is used in loop it fails? Why it is happening? Is there any mathematics
behind that?



Orestis Chrysafis wrote:
> 
> Dear R experts
> I need to write a function that incorporates double summation, the problem
> being that the upper limit of the second summation is the index of the
> first
> summation, i.e:
> 
> sum_{j=0}^{x} sum_{i=0}^{j} choose(i+j, i)
> 
> where x variable or constant, doesn't matter.
> The following code obviously doesn't work:
> 
> f=function(x) {j=0:x; i=0:j; sum( choose(i+j,i) )  }
> 
> Can you help?
> Thanks in advance,
> 
> Orestis Chrysafis
> School of Mathematics
> University of Sheffield
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
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> and provide commented, minimal, self-contained, reproducible code.
> 
> 

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