% Define length of the sequence
N = 20;

% Preallocate output vector
x = zeros(N,1);

% Define input (unit step)
u = ones(N,1);

% Initial conditions
x(1) = 1; % x(0)
x(2) = 2; % x(1)

% Calculate the output iteratively using the given expression
for k = 2:N-1
  x(k+1) = 2 + 4*u(k-1) - (0.5)^(k-1)*u(k-1);
end

% Create a vector for plotting
k = 0:N-1;

% Plot the resulting sequence
figure;
stem(k, x, 'filled');
grid on;
xlabel('Time step (k)');
ylim([0,10])
ylabel('x[k]');
title('Solution of the Difference Equation with Given Input and Initial Conditions');