Is there a simpler Seq.unfold version that just takes the previous element as the state? I know you can easily adapt Seq.unfold to do that, but the result is not very readable.
I don't think there is a built-in function that does that.
Repeating the same pattern using Seq.unfold would be quite annoying, but you can easily use unfold to define a function that behaves as you want and then just use the new function:
module Seq =
let generate f v =
Seq.unfold (fun v -> let r = f v in Some(r, r)) v
As an aside, if I wanted to implement the pattern, I would probably go with a simple recursive sequence expression, which might be easier to read than using Seq.unfold. The generate function can be implemented like this:
let rec generate f v = seq {
yield v
yield! generate f (f v) }
This behaves a bit differently, because it yields the first value as well. Not sure what behaviour you want.