import itertools
def golden(n):
    out=[[]]
    for _ in range(n):
        out=[s+[b] for s in out for b in (0,1) if not (b==1 and s and s[-1]==1)]
    return out
def row(u,K):
    # C_0 alternating (dark at even t); C_1 = x_-1: even t -> not u_n, odd t -> 1
    T=2*len(u)
    C0=[t%2 for t in range(T+2)]
    C1=[(1-u[t//2]) if t%2==0 else 1 for t in range(T)]
    prev,cur=C0[:T],C1; out=[cur[0]]
    for k in range(1,K):
        nxt=[cur[t+1]^(cur[t]|prev[t]) for t in range(len(cur)-1)]; prev,cur=cur,nxt; out.append(cur[0])
    return out
LOOK=3; OUTS=6
for n in range(4,17,2):
    sigs=set()
    conts=[c for c in golden(LOOK)]
    for p in golden(n):
        sig=[]
        for c in conts:
            if p and p[-1]==1 and c[0]==1: sig.append(None); continue
            u=p+c+[0]*4
            r=row(u,2*(n+LOOK))
            sig.append(tuple(r[2*n:2*n+OUTS]))
        sigs.add(tuple(sig))
    print(f"prefix length {n:2d}: admissible prefixes {len(golden(n)):5d}, distinguishable futures {len(sigs):5d}")