Nobody knows GAU Numbers Let me introduce you to GAU numbers
GAU(1) = 1  
GAU(2) = 1122  
GAU(3) = 1122122333  
GAU(4) = 11221223331223334444  
GAU(6) = 11221223331223334444122333444455555122333444455555666666  
...  
GAU(10) = 11221223331223334444122333444455555122333444455555666666122333444455555666666777777712233344445555566666677777778888888812233344445555566666677777778888888899999999912233344445555566666677777778888888899999999910101010101010101010  

This challenge is pretty simple!
Given an integer n&gt;0, find the number of digits of GAU(n)
Example
Let's make GAU(4)
we take the following steps (until we get to 4) and concatenate them
[1][122][122333][1223334444]   

you must write every number as many times as its value, but you have to count every time from 1
Let's try to make GAU(5)
we will have to count from 1 to 1
[1]   

then from 1 to 2 (but repeating every number as many times as its value)
[122]     

then from 1 to 3
[122333]   

then from 1 to 4
[1223334444]    

and finally from 1 to 5 (this is the last step because we want to find GAU(5))
[122333444455555]     

Now we take all these steps and concatenate them
the result is GAU(5)
11221223331223334444122333444455555     

We are interested in the number of digits of these GAU numbers.
Test cases
Input⟼Output
n   ⟼ Length(GAU(n))

1   ⟼ 1  
2   ⟼ 4  
3   ⟼ 10  
10  ⟼ 230   
50  ⟼ 42190  
100 ⟼ 339240  
150 ⟼ 1295790  

This is a code-golf challenge.
Shortest code in bytes will win.
If you still have any questions please let me know.
I really want everyone here to understand this magic-hidden-complex pattern
SOGL V0.12, 11 10 8 7 5 bytes
∫∫l*+

Try it Here! - this expects to be called as a function with the input on the stack and the input box empty.
7 byte alternative taking the input from the input box:
0.∫∫l*+

Try it Here!
0      push 0
 .     push the input
  ∫    iterate over a range 1..POP (input) inclusive, pusing the current number
   ∫    iterate over 1..POP (above loops number) inclusive, pusing the current number
    l    push that numbers length without popping the number
     *   multiply the length by the number
      +  add to the zero, or whatever it is now