We were reviewing Monte Carlo Simulation of Synthetic Data Sets shortly. This is a powerful technique. It assumes that if the fitted parameters a0 is a reasonable estimate of the true parameters by minimizing the chi-square then the distribution of difference in subsequent parameters from a0 should be similar to that of the corresponding calculation with true parameters

#codingexercise
Find the Delannoy number
This number describes the number of paths from the southwest corner (0,0) of a rectangular grid to the northeast corner (m,n) using only single steps north, northeast or east
In a 3 by 3 square there are 63 paths from bottom left to top right corner using the above method.
The recursion for this is calculated as
D(m,n) = 1 if m == 0 or n == 0
             = D(m-1, n) + D(m-1, n-1) + D(m, n-1) for the three different paths permitted

int GetDelannoy(int n, int m)
{
    if (m == 0 || n == 0)
        return 1;

    return GetDelannoy(m - 1, n) +
               GetDelannoy(m - 1, n - 1) +
               GetDelannoy(m, n - 1);
}
>>> def d(m,n):
...     if ((m==0) or (n==0)):
...         return 1
...     return d(m-1,n)+d(m-1,n-1)+d(m,n-1)
...
>>> print d(3,3)
63
>>> print d(4,4)
321
The recursion tree has a maximum depth of m + n