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这个是smark news 第一面的题目

# #
# # For an int N (N>0), figure out how many ways you can split it into one or mutiple adders.
# # 1) adder > 0 int
# # 2) adder order does not matter
# #
# # 1 = 1
# # S(1) = 1
# #
# # 2 = 2
# # 2 = 1 + 1
# # S(2) = 2
# #

# # 3：
# # 3 = 3
# # 3 = 2 + 1
# # 3 = 1 + 1 + 1
# # S(3) = 3
#

# # 4 :
# # 1) 4 = 4
# # 2) 4 = 3 + 1
# # 3) 4 = 2 + 2
# # 4) 4 = 2 + 1 + 1
# # 5) 4 = 1 + 1 + 1 + 1
#
# # S(4) = 5
#


# # 5:
# # 5 = 5
# # 5 = 4(5-1) + 1      
# # 5 = 3(5-2) + 2
# # 5 = 3 + 1 + 1  
# # 5 = 2 + 2 + 1 = 1 + 2 + 2
# # 5 = 2 + 1 + 1 + 1
# # 5 = 1 + 1 + 1 + 1 + 1
# # S(5) = 7
#


# # 6:
# # 6 = 6
# # 6 = 5 + 1
# # 6 = 4 + 2
# # 6 = 4 + 1 + 1
# # 6 = 3 + 2 + 1
# # 6 = 3 + 1 + 1 + 1
# # 6 = 3 + 3
# # 6 = 2 + 2 + 2；
# # 6 = 2 + 2 + 1 + 1；
# # 6 = 2 + 1 + 1 + 1 + 1；
# # 6 = 1 + 1 + 1 + 1 + 1

#7 = 7
#7 = 6 + 1
#7 = 5 + 2
#7 = 5 + 1 + 1
#7 = 4 + 3
#7 = 4 + 2 + 1
#7 = 4 + 1 + 1 + 1
#7 = 3 + 3 + 1
#7 = 3 + 2 + 2
#7 = 3 + 2 + 1 + 1
#7 = 3 + 1 + 1 + 1 + 1
#7 = 2
#

# # S(6) = 11
# #
# # S(n) = ?