4ct.js

function prodf(xs, ys, f) {
  const rv = [];
  for (let i = 0; i < xs.length; i++) {
	 for (let j = 0; j < ys.length; j++) {
		rv.push(f(xs[i], ys[j]));
	 }
  }
  return rv;
}

function list(n) {
  if (n == 0) {
	 return [];
  }
  if (n == 1) {
	 return ['x'];
  }
  else {
	 let rv = [];
	 for (let i = 1; i <= n - 1; i++) {
		rv = rv.concat(prodf(list(i), list(n-i), (a, b) => [a,b]));
	 }
	 return rv;
  }
}

function colorings(tree, c) {
  if (tree == 'x') return [c + ''];
  else {
	 const opts1 = prodf(colorings(tree[0], (c + 1) % 3), colorings(tree[1], (c + 2) % 3), (a, b) => a + b);
	 const opts2 = prodf(colorings(tree[0], (c + 2) % 3), colorings(tree[1], (c + 1) % 3), (a, b) => a + b);
	 return opts1.concat(opts2);
  }
}

// x is a string over 0, 1, 2
function canonical(x) {
  function rewrite(x, p) {
	 return x.replace(/./g, c => p[parseInt(c)]);
  }
  return ['012', '021', '201', '210', '120', '102'].map(p => rewrite(x, p)).sort()[0];
}

function cstring(t) {
  return [...new Set(colorings(t, 0).map(canonical))].sort().join('-');
}

function intersect(s1, s2) {
  let count = 0;
  for (const c of s1) {
	 if (s2.has(c)) count++;
  }
  return count;
}

const i = 8;
const css = list(i).map(cstring).map(s => new Set(s.split('-')));
for (let j = 0; j < css.length; j++) {
  let s = '';
  for (let k = 0; k < css.length; k++) {
	 s += ' ' + intersect(css[j], css[k]);
  }
  console.log(s);
}