% Implement Fibonacci sequence by using a while loop

clear all
close all
clc

u_1=1;
u_2=1;
u_v=[u_1 u_2]; %initial sequence

% start to compute the recursive relation at time k=3 
k=3;

% for idx_k=k:tk_f
%     u_k=u_v(idx_k-1)+u_v(idx_k-2);
%     u_v_old=u_v;
%     u_v=[u_v_old u_k];
% end

tk_f=9; % final time

while k<=tk_f
    u_k=u_v(end)+u_v(end-1); % recursive relation
    u_v_old=u_v;
    u_v=[u_v_old u_k];
    clear u_v_old
    k=k+1;
end

% define time
time_k=1:tk_f; % time vector

% plot the sequence
figure
plot (time_k,u_v,'dr','MarkerSize',8,'LineWidth',3)
xlabel('time k')
ylabel('u_k')
set(gca,'FontSize',16)
grid on