# [R] Double summation limits

David Winsemius dwinsemius at comcast.net
Sat May 2 06:39:23 CEST 2009

```On May 2, 2009, at 12:18 AM, RON70 wrote:

>
> 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?

What loop? You made j a vector and then tried to treat it like a
single value. You even got an informative error message:
"Warning message:
In 0:j : numerical expression has 4 elements: only the first used"

> 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?
>>
>> Orestis Chrysafis
>> School of Mathematics
>> University of Sheffield

David Winsemius, MD
Heritage Laboratories
West Hartford, CT

```