Double summation limits
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