IMO Shortlist 2002 problem C3
Kvaliteta:
Avg: 0,0Težina:
Avg: 7,0 Let
be a positive integer. A sequence of
positive integers (not necessarily distinct) is called full if it satisfies the following condition: for each positive integer
, if the number
appears in the sequence then so does the number
, and moreover the first occurrence of
comes before the last occurrence of
. For each
, how many full sequences are there ?
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![k\geq2](/media/m/6/9/c/69c4170fa46a91b6265eb781bcaf2f6c.png)
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
![k-1](/media/m/e/2/5/e2582f1a41d7cbbc089069312ee7488a.png)
![k-1](/media/m/e/2/5/e2582f1a41d7cbbc089069312ee7488a.png)
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
Izvor: Međunarodna matematička olimpijada, shortlist 2002