Arrayfun - for conversion

I want to replace for loop with arrayfun but i don't have idea. In this case there is a particular dependence the two foor's. Every element X(k+1) dependes from X(k), X(k-1),.....X(k-limit). The presence of min() function makes the index k-p always positive.

X(1)= first_step;
for k=1:length_1
for p=0:min(k-1,length_2)
X(k+1)=X(k+1)+j(p+1)*X(k-p)
end
end

My aim is to fit this code for GPU computing