Algorithm



Hello,
I would like to know how I could implement an algorithm in maxima.
I want run the following algorithm;

"   Initialize: d=(3+sqrt(8))^n;  d=(d+1/d)/2;
         b=-1;  c=-d;  s=0;
    For k=0 up to k=n-1, repeat:
         c=b-c;  s=s+c*a_k;
         b=(k+n)*(k-n)*b/((k+0.5)*(k+1));
    Output: s/d.                                "

I am attaching the original PDF file of the algorithm. The one I want to run
in maxima is 'Algorithm 1'.

Thank you.