without_two_zeros.js

const splitByPairs = (x) => {
  const pairsCount = x.length - 1;
  
  return new Array(pairsCount).fill().map((index, val) => x.substr(val, 2));
};

const digitsCount = (digit, number) => number.split('').filter(num => num == digit).length;

const dec2bin = (dec) => { return (dec >>> 0).toString(2) };

const range = (l, r) => new Array(r - 1).fill().map((_,k) => k + l);

const fillByZeroes = (x, to) => {
  const numLength = (x).toString().length;
  if (numLength >= to) {
    return x;
  }
  
  const zeroLacks = to - numLength;
  
  return '0'.repeat(zeroLacks).concat((x).toString());
};

const withoutTwoZeros = (x, y) => {
  const pow = x + y;
  if(x == 1 && y == 1) {
    return 2;
  }
  
  const zeroOnesColl = range(1, Math.pow(2, pow))
    .map(x => dec2bin(x))
    .map(x => fillByZeroes(x, pow));
  
  //return zeroOnesColl; 
  const filtered = zeroOnesColl.filter(el => {
    return digitsCount(0, el) == x && digitsCount(1, el) == y;
  });
  
  return filtered
    .map(x => splitByPairs((x).toString()))
    .filter(pairs => pairs.indexOf('00') == -1)
    .length
};

console.log(withoutTwoZeros(2, 2)); // 3
console.log(withoutTwoZeros(1, 1)); // 2
console.log(withoutTwoZeros(1, 3)); // 4
console.log(withoutTwoZeros(2, 4)); // 10