Difference in values of output by manual and code

I am trying to solve a difference equation with initial conditions using 'filter' function. The manual calculation of y(n) and the one procuced by 'fliter' seems to have some difference. What is the error.

The code is shown below:

disp('Solution of a difference equation:')
% The example difference equation considered is
% y(n) = 0.5y(n-1) + x(n) 
num_coef = [ 1 ]; % coefficient of x
den_coef = [1 -0.5]; % coefficient of y

n = 0:4; % Considering five samples 
x = 6 * ones(1,5) % x(n) = 6u(n)
init_cond = [1];  % y(-1) = 1
y = filter(num_coef, den_coef, x, init_cond) % Solution returned by 'filter'
yM = 12 - (11/2)*(1/2).^n % Solution obtained manually
plot(y);hold on; % PLots for comparison
plot(yM,'r')

[David Wilson]

I've always had trouble with the intial condition which is where I think your problem lies. Note that Zi (in the help) is the initial delay, not the initial value of the y.

[prashanth A]

Do I have to delay the signal? How did you solve it?