stair.js

// get postitive sequence values
// n - index of value in sequence
// x - array of values describing function
// general function: f(n) = f(n - x[0]) + f(n - x[1]) + ... + f(n - x[m]); f(0) = 1;

function stair(n, x, cache)
{
  cache = cache || [1];
  
  if (cache[n]){
    return cache[n];
  }
  
  if (n < 0){
    return 0;
  }
  
  
  var res = 0;
  for (var k in x){
    res +=  stair(n - x[k], x, cache);
  }
  
  document.write('Possible arrange ways for n='+ n +': '+ res +'<br>');
  cache[n]  = res;
  return res;
}




document.write('<h3>'+ stair(5000, [10]) +'</h3>');