Jumping steps problem (javascript)

index.js

/*
A flight of stairs has `n` steps, you are able to jump 1, 2, or 3 steps at a time.
How many different ways are you able to climb the stairs in different combinations of jumps?

E.g. n = 3 then the answer is 4 because: 111, 21, 12, 3
*/

const replaceIndexWithNum = (str, i, num) => {
	return str.substring(0, i)+num+str.substring(i+num)
}

/**
 * consumeAndIterate will loop through `str` replacing: 11 with 2 and 111 with 3
 * then call itself with the resulting string to recurse until all 
 * combinations are found. Therefore results can be found like a tree structure
 *
 * It will mutate the `results` object e.g.
 * consumeAnditerate(3, '111', {}) => {'111': true, '21': true, '3': true, '12': true }
 */
const consumeAndIterate = (n, str, results = {}) => {
  results[str] = true

  for (let i = 0; i < str.length; i++) {
    const add2 = parseInt(str[i]) + parseInt(str[i+1])
    const strWith2 = replaceIndexWithNum(str, i, 2)
    if (add2 === 2 && !results[strWith2]) {
      consumeAndIterate(n, strWith2, results)
    }

    const add3 = add2 + parseInt(str[i+2])
    const strWith3 = replaceIndexWithNum(str, i, 3)
    if (add3 === 3 && !results[strWith3]) {
      consumeAndIterate(n, strWith3, results)
    }
  }

  return results
}

const solution = (n) => {
  // start recursing with string of 1s
  const results = consumeAndIterate(n, Array(n).fill(1).join(''))
  return Object.keys(result).length
}