I have the following Values: $a[0]=1;a[1]=0;a[2]=0;a[3]=0;a[4]=\frac{g_2}{20};a[5]=0$.
I need to compute the value of $b[n]$ in the following equation
$$a[n]=\sum _{m=0}^{n} (m-2) \;\;a[m] \;\;b[n-m]$$ where $n=0,1,2,3,4,5$.
For $n=0$, I get the value of $b[0]$.
For $n=1$, I get the value of $b[1]$ using the value of $b[0]$.
For $n$th iteration, I get the value of $b[n]$ using the values of $b[n-1],b[n-2],\dots,b[0]$.
The values of $b[n]$ will then be used to solve for another variable, say, $c[n]$, for $n=0,1,2,3,4,5$.
Is there any simple way of doing this in Mathematica? I am basically doing one iteration at a time (using the Solve command), which is very tedious.
Thanks, Radz.