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Problems > High School Math > 2003

Interesting Integer Sequences

Let A be the set of all possible finite sequences (n0, n1, ..., nk) of integers such that,


for each i = 0, 1, ..., k


i appears in the sequence ni times.

 

Here are some sequences in set A:

 

 

1,2,1,0

2,0,2,0

2,1,2,0,0

3,2,1,1,0,0,0

4,2,1,0,1,0,0,0

k-3,2,1,0,0,...,1,0,0,0

 

 

Are there other sequences in set A? If so, what are they?

 

 

Now prove it.

 



View the solution
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