How many coins are possible?

Calvin put 2001 coins of 1, 2 or 3 dollars in a row. It turned out that between any two 1-dollar coins there is at least one coin; between any two 2-dollar coins there are at least two coins; and between any two 3-dollar coins there are at least 3 coins. There are \(k\) three dollar coins. How many values of \(k\) are possible?


Image Credit: Flickr Jamal Ashiqain.
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