# [Jelly], <s>7</s> 6 bytes

    3rc3«i

[Try it online!]

### How it works (outdated)

    R‘c3<¹S  Main link. Argument: n

    R        Range; yield [1, ..., n].
     ‘       Increment; yield [2, ..., n+1].
      c3     Combinations; yield [C(2,3), ..., C(n+1,3)].
        <¹   Yield [C(2,3) < n, ..., C(n+1,3) < n].
          S  Sum; count the non-negative values of k for which C(k+2,3) < n.

[Jelly]: https://github.com/DennisMitchell/jelly
[Try it online!]: https://tio.run/nexus/jelly#@29clGx8aHXm/6N7Drc/alrj/v@/oY6CqY6CORAbGhjoKBgZgQmgqLGZCQA "Jelly – TIO Nexus"