🚀 go-pugleaf

Hi, 

I have a question as follows:

A person would like to go from a to b in the following diagram,
one step at a time. No retrieving back or standing still is 
allowed so that the total no. of steps is always (X+Y) Steps. There
are many alternative routes between a and b by changing the
sequence of X direction steps and Y direction. For example, the
route can be a->c->b or a->d->b or a->e->f->g->h->i->j->b.
What is the total number of routes all together? Is there a
close formular or function of X and Y? Is it a classical
Graph Theory question that I can find in some books?

Hint: I found out an algorithm which can be implemented in computer
      programming, but I cannot get a close formular.

Tm,n --- Total number of routes in a m step by n step rectangle.

Tx,y = (Tx-1,y) + (Tx,y-1)

T1,1 = 2
T1,2 = T2,1 = 3
T2,2 = 6



      c	|<--- X Steps ----->| b
	+----+----+----+----+ -
	|    |    |    |    | ^
	|    |    |h   |i  j| |
	+----+----+----+----+ 
	|    |    |    |    | Y Steps
	|    |f   |g   |    |
	+----+----+----+----+
	|    |    |    |    | |
	|    |    |    |    | V
	+----+----+----+----+ -
	a    e                d


If you have any idea, please send me an email to make sure that I 
receive it. (liuf@bnr.ca) Thanks a lot.


Regards,
Frank Liu