Generate the Stöhr sequence

APL, 7

In APL you can choose if you want to work with index 0 or index 1. You do this by setting global variable ⎕IO←0

If we choose to work in index 0 we have:

+\3⌊1⌈⍳

Explanation:

⍳    creates a sequence 0...n   (0 1 2 3 4 5)
1⌈   takes whichever is bigger, number in sequence or 1 (1 1 2 3 4 5)
3⌊   takes whichever is lower, number in sequence or 3 (1 1 2 3 3 3)
+\   partial sums for the sequence (1 2 4 7 10 13)

Try it on tryapl.org

Haskell - 11 21

Lazy infinite sequence

1:2:[4,7..]

Function that returns just supplied number of members (sigh)

flip take$1:2:[4,7..]

Python 2, 37 35 bytes

lambda n:[1,2][:n]+range(4,n*3-4,3)

Making use of a pattern...