Number of unique corners for given color / dot schemes

permutations.js

const uniq = require('lodash/uniq');

function permutations(n, colors, arr) {
  if (!n) return [arr];
  if (!arr) arr = [];
  let ret = [];
  for (let i = 0; i < colors; i++) ret = ret.concat(permutations(n - 1, colors, arr.concat([i])));
  return ret;
}

console.log(
  'Code240 (Dynamicland; per corner):',
  permutations(5, 4).filter(colors => uniq(colors).length >= 4).length
);
console.log(
  'Paper Programs v1:',
  permutations(5, 5).length / 5
);
console.log(
  'Double dots with unique corners and each color in a corner at least once:',
  permutations(8, 4).filter(colors => uniq(colors).length >= 4).length / 4
);