Eqn =
Perhaps something like this —
syms n x(n) y(n) z t X(z) Y(z)
assume(n>=0 & in(n,"integer"))
Eqn = y(n) == 0.5*y(n - 1) + x(n)
Eqn = ztrans(Eqn, n, z)
Eqn = subs(Eqn, {ztrans(y(n),n,z), ztrans(x(n),n,z)}, {Y(z), X(z)})
Eqn = isolate(Eqn, Y)
[N,D] = numden(rhs(Eqn))
Nc = sym2cell(N)
Dc = sym2cell(D)
I leave the rest to you!
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