Date: Jun 30, 2013 7:52 AM
Author: Alin Soare
Subject: Singularities in Pascal Triangle.
I have this problem:

Compute the numbers in the Pascal Triangle, but on some positions (X,Y), the pascal triangle has 0, instead of the sum of P(X, Y-1) + P(X-1, Y-1) , each time when X is in relation R with Y.

Obviously, if I am asked to compute the Pascal Triangle, I do not recursivelly compute the sums for each pair, but I compute the combinations(X,Y).

I wish to ask you whether the methods of analytic combinatorics can help to solve this problem -- to find the values using some analytical formula instead of recurrence.