utopianTree.js

 /*
 * @desc https://www.hackerrank.com/challenges/utopian-tree
 * @param integer n 
 * @return integer of the height of the Utopian Tree after n cycles
 */

function utree (n) {
  
  if(n===0){
    return 1;
  }
  
  // a(n) = a(n-1) (+ 1 || * 2)
  
  var tail = utree(n-1);
  if(n%2){
    return 2*tail;
  }else{
    return 1+tail;
  }
   
}