Подсчет уникальных наборов?

Я решал эту проблему: http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=286&page=show_problem&problem=3268
и я застрял и не могу найти никаких подсказок.
Вопрос:

 You will be given an integer n ( n<=10^9 ) now you have to tell how many
 distinct sets of integers are there such that each number from 1 to n can
 be generated uniquely from a set. Also sum of set should be n. eg for n=5 , one such set is:
 {1,2,2} as
 1 can be generated only by  { 1 }
 2 by { 2 }
 3 by {1,2} ( note the two 2's are indistinguishable)
 4 by {2,2}
 5 by {1,2,2}
 for generating a number each number of a set can be used only once. ie for above set
 we can't do {1,1} to generate 2 as only one 1 is there.
 Also the set {1,2,2} is equivalent to {2,1,2} ie sets are unordered.

Мой подход:

 The conclusion I came to was. Let F(S,k) denote number desired sets of sum S whose 
 largest element is k.Then to construct a valid set we can take two paths from this
state.Either to F(S+k,k) or to F(2*S+1,S+1).I keep a count of how many times I come
to state where S=n(the desired sum) and do not go further if S becomes > n.This is  
clearly bruteforce which I just wrote to see if my logic was correct(which is correct)
.But this will give time limit exceed . How do I improve my approach??I have a 
feeling  it is done by dp/memoization.