Writing a Recursive Function

I am having trouble writing a recursive function that calculates the value of N(i,p)

for example, to calculate N(0,2), I need the values of N(0,1) and N(1,1). Then each of those will need the values of the lower nodes in the tree as shown below. The value of any N(i,0)=1.

Answer 1

[Mathieu NOE]

hello

see below

Nb : matlab is not a zero based indexing language , so first index is 1 instead of 0

%% initialisation 
n = 5;
N = zeros(n,n);
N(1,1:n)  = 1; % (all N(i,0) = 1)

%% main loop
for p = 2:n
    ind_i = 1:1+n-p; % index of i is function of p (it reduces as index p increases)
    N(p,ind_i) = N(p-1,ind_i) + N(p-1,ind_i+1);
end

% display lines in reversed order 

N = N(n:-1:1,:)

[Mahmoud Abbas]

Wow, Thank You!

[Mathieu NOE]

My pleasure !

Answer 2

[Mathieu NOE]

the results appears like this for n = 5

N =

16 0 0 0 0

8 8 0 0 0

4 4 4 0 0

2 2 2 2 0

1 1 1 1 1

the bottom line is the starting values (Ni,o = 1)