The number 1 is written on the blackboard. After that a sequence of numbers is created as follows: at each step each number a on the blackboard is replaced by the numbers aā1 and a+1; if the number 0 occurs, it is erased immediately; if a number occurs more than once, all its occurrences are left on the blackboard. Thus the blackboard will show 1 after 0 steps; 2 after 1 step; 1,3 after 2 steps; 2,2,4 after 3 steps, and so on. How many numbers will there be on the blackboard after n steps? inductioncombinatorics unsolvedcombinatorics