Hi, need some help with my thesis The multimensional binomial method

I have used the code from Implementing derivatives models, clewlow and chris Strickland, pp_ 44. I have problems understanding the for command that he uses in Pseudo-code. The answer is 5.3269

can anyone please help?

% American Call Option by Two-varible Binomial 
clc, clear all

%input
K = 1;
T = 1;
S1 = 100;
S2 = 100;
sig1 = 0.2;
sig2 = 0.3;
div1 = 0.03;
div2 = 0.04;
rho = 0.5;
r = 0.06;
N = 3;

%precompute constants
dt = T/N;
nu1 = r - div1 - 0.5*sig1^2         %risk neutral process
nu2 = r - div2 - 0.5*sig2^2         %risk neutral process
dx1 = sig1*sqrt(dt)                 
dx2 = sig2*sqrt(dt)                 
disc = exp(-r*dt)

puu = (dx1*dx2 + (dx2*nu1 + dx1*nu2 + rho*sig1*sig2)*dt)/ (4*dx1*dx2)*disc      %Risk index up, Oil Up 

pud = (dx1*dx2 + (dx2*nu1 - dx1*nu2 - rho*sig1*sig2)*dt)/ (4*dx1*dx2)*disc      %Risk index up, oil Down

pdu = (dx1*dx2 + (-dx2*nu1 + dx1*nu2 - rho*sig1*sig2)*dt) / (4*dx1*dx2)*disc    %Risk index down, Oil Up

pdd = (dx1*dx2 + (-dx2*nu1 - dx1*nu2 + rho*sig1*sig2)*dt) / (4*dx1*dx2)*disc    %Risk index down, Oil Down

edx1 = exp(dx1)     %prop. increase if up movement
edx2 = exp(dx2)     %prop. increase if up movement

%initialise asset prices at time step N
S1(N+1) = S1*exp(-N*dx1);
S2(N+1) = S2*exp(-N*dx2);
for j = N:1:N
    S1(j) = S1(j+1)*edx1
    S2(j) = S2(j+1)*edx2
end

%initialise option values at maturity
for j = 1:1:N+1
    for k = 1:1:N+1
       c(j,k) = max(0.0, S1(j)-S2(k) - K)
    end
end

%step back through the tree applying early exercise 

for i = N+1:1:0
    for j = 1:1:i
       for k = 1:1:i
            c(j,k) = pdd*c(j-1,k-1) + pud*c(j+1,k-1) + pdu*c(j-1, k+1) + puu*c(j+1,k+1)
            c(j,k) = max(c(j,k), S1(j) -S2(k)- K)
       end
    end
end

American_spread_option = c(0,0)