How to create a sequence of numbers with repeat and increment at intervals in google sheets

I need a single cell formula to create a sequence of numbers with a limit in Google Sheets as shown in the image.

3 rows repeat the value

then Increment by 5

Solution

Use this formula, you can adjust the Sequence() and REPT(rg&",",3) parameters to your need.

In this example Sequence(number_of_unique_numbers,columns,start_at,increment_by)

And REPT(rg&",",Repeat_N_times)

=ArrayFormula(FLATTEN(SPLIT(BYROW(SEQUENCE(3,1,5,5), 
 LAMBDA(rg, IF(rg="",,REPT(rg&",",3)))),",")))

Option 02
Based on Themaster - answer we use lambda with the names.
u unique
s start
r repat n time

=LAMBDA(u,s,r, FLATTEN(MAKEARRAY(u,r,LAMBDA(u,r,u*s))))
       (4,5,3)