



 
Consider two simplifications: The number of nondecreasing sequences of size at least 1 and at most N, = The number of nondecreasing sequences of size at least 1 and at most N, = (The number of nondecreasing sequences of size EXACTLY N, The first simplification is because you can then add (L1) to every The second simplification is that if a sequence starts with 0, you The next step is to get rid of the ordering: If you get a bunch of N Let X(0) be the numbers of zeros in the bunch, X(1) the number of ones, To figure it out, it is best to represent the numbers by sticks: Each sum corresponds to an permutation of sticks and plus signs. Claude  


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