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]]
Perhaps:
SSCxy <- function(z) {tail(sapply(0:z, function (x) sum(sapply(0:x,
function(y) sum(choose(x+y, y))))), 1) }
> SSCxy(5)
[1] 462
See also:
http://www.research.att.com/~njas/sequences/?q=1%2C3%2C10%2C35%2C126%2C462&sort=0&fmt=0&language=english&go=Search
On May 1, 2009, at 3:45 PM, 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
David Winsemius, MD
Heritage Laboratories
West Hartford, CT
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]] > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > >-- View this message in context: http://www.nabble.com/Double-summation-limits-tp23341171p23342887.html Sent from the R help mailing list archive at Nabble.com.