How many unique one sided polyominos Context

From Wikipedia:
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge.

one-sided polyominoes are distinct when none is a translation or rotation of another (pieces that cannot be flipped over). Translating or rotating a one-sided polyomino does not change its shape.

In other words, a one sided polyomino reflected across its x or y axis is not the same as the original polyomino, but a one sided polyomino that is rotated is still considered the same polyomino

Task

Given a number n, find how many different unique one sided 
polyominos can be created using n number of blocks

Input

Take integer n as input for the number of blocks that exist in the polyomino

Output

An integer of the amount of unique one sided polyominos that can be generated

Examples

in -> out

4 -> 7

5 -> 18

6 -> 60

7 -> 196

More test cases can be found on the Wikipedia page and OEIS
Jelly,  39  37 bytes
Soon to be crushed by MATL and, quite possibly, APL
p`œc⁸ḣ1ạ§ỊẸʋƇ@;QɗƬƊṪṢƊƑƇŒṬZṚŒṪƲƬṂ$€QL

Try it online! (It's pretty slow - a(6) took ~30 minutes locally!)
To see them instead try this (L -&gt; ŒṬ€G€j⁾¶¶).
How?
Builds all index lists, where each represents the locations of 1s on a grid of 1s and 0s, up to those for a square of side n, filters for those that have their 1s fully connected, then selects the &quot;minimal&quot; of each after any amount of rotation + vertical translation, and finally de-duplicates and yields the length.
   p`œc⁸ḣ1ạ§ỊẸʋƇ@;QɗƬƊṪṢƊƑƇŒṬZṚŒṪƲƬṂ$€QL - Link: integer, n
   A....B..................C............ - break down below
    
A: p`œc⁸ - Get all ways to have n 1s on an n*n grid as multidimensional indices
    `    - use n as both arguments of:
   p     -   Cartesian product -&gt; all pairs of [1..n] - these are in sorted order
       ⁸ - chain's left argument, n
  œc     - combinations (no replacement) - ...and so each of these are in sorted order

B: ḣ1ạ§ỊẸʋƇ@;QɗƬƊṪṢƊƑƇ - Keep only the fully-connected ones (call input &quot;All&quot;)
                     Ƈ - filter keep those for which:
                    Ƒ  -   is invariant under:
                   Ɗ   -     last three links as a monad:
                Ɗ      -       last three links as a monad:
    1                  -         one
   ḣ                   -         head to index - i.e. [firstPair] (initial &quot;Current&quot;)
               Ƭ       -         collect up while distinct, applying:
              ɗ        -           last three links as a dyad - i.e. f(Current, All):
           @           -             with swapped arguments - i.e. f(All, Current):
          Ƈ            -               filter keep those (of All) for which:
         ʋ             -                 last four links as a dyad - i.e. f(All, Current):
     ạ                 -                   absolute difference (vectorises)
      §                -                   sum each
       Ị               -                   insignificant? (effectively &quot;in (0,1)?&quot;)
        Ẹ              -                   any? - i.e. any are neighbours/same?
            ;          -             concatenate (the result with Current)
             Q         -             deduplicate (-&gt; Current for the next Ƭ-loop)
                 Ṫ     -       tail
                  Ṣ    -       sort

C: ŒṬZṚŒṪƲƬṂ$€QL - Count the distinct results
             €   - for each:
            $    - last two links as a monad:
          Ƭ      -   collect up while distinct, applying:
         Ʋ       -     last four links as a monad:
   ŒṬ            -       2d array from multidimensional indices
     Z           -       transpose
      Ṛ          -       reverse (transpose + reverse = rotate 1/4 anti-clockwise)
       ŒṪ        -       truthy multidimensional indices
           Ṃ     -   minimum
              Q  - de-duplicate
               L - length