Substitution to make it simple...

there is recursive sequence and v(2)=...v(1) and v(3)=...v(2)+...v(1) and so on... i want to remove v(2) and replace it with v(2)=...v(1) , at the other hand i need v(3) to be just function of v(1). take a look at the code...

%
%%Initialization
clc;clear all;
VLL=63;
Vph=VLL/(sqrt(3));
N=5;
m=10;
n=5;
%%Body
syms v(k) 
flag=0;
for counter=2:N
  if counter==2
      disp(['Number',num2str(counter)])
      v=symfun([(2+1/m)*v(k-1)],k);
      v(counter)
      clear v
  else
  syms v(k) 
  disp(['Number',num2str(counter)])
  v=symfun([(2+1/m)*v(k-1)]-v(k-2),k);
  v(counter)
  end
  end
end