Fibonacci sequence (http://en.wikipedia.org/wiki/Fibonacci_number) sum http://jsbin.com/iqomew/2/edit, diversity tests http://jsperf.com/fibonacci-perfomance/5

fibonnaciSum.js

function fibonacciSum(n) {
	'use strict';
	var
		sequence = fibonacci(n);

	return sequence.reduce(function(a, b) {
		return a + b;
	});
}

fibsum.js

function fibsum(n) {
  var fib = [],
      sum = 0,
      cur,
      prev = 0,
      prevprev = 0;
  for(; n--;) {
    cur = prev + prevprev || 1;
    prevprev = prev;
    prev = cur;
    fib.push(cur);
    sum += cur;
  }
  // console.log(fib, sum);
  return sum;
}

console.log(fibsum (10));

sequenceFinder.js

function fibonacci(n) {
	'use strict';
	var
		out = [1];

    function fibSeq(seq, i) {
    	var
    		item;

    	if ( i < n ) {

    		item = seq[i - 1] + seq[i - 2];
    		seq.push(item);
    		fibSeq(seq, seq.length);
    	}

    	return seq;
    }

    if ( n >= 2 ) {

    	fibSeq([1,1], 2);
    } else if ( n === 1 ) {

    	out = out.push(1);
    }

    return out;
}

function christmasPresents (days, current = 0, collect = [0]) {
	if (current < days) {
		collect.push(current + )
		christmasPresents(days, current + 1, collect)
	}
	return collect
}

var answer = christmasPresents(12)
console.log(answer)