Build a triangle without any triangles As a little kid, I liked to play with these toys a lot:



They probably intended for these to be used for art, but I always used them for math! Fractals, patterns, etc. One time, I was given this challenge:


  Build a triangle without using any of the green triangle tiles.


This challenge stumped me for the longest time, until I stumbled upon a really beautiful and simple way to do it with just 3 trapezoids:

  /\  
 /_/\ 
/__\_\


Now, take this triangle, and rotate it:

______         
\ \__/         
 \/ /          
  \/ 


Using these two triangles, we can construct larger triangles out of them. Here is a triangle of height 2:

     /\           
    /_/\          
   /__\_\         
  /\ \__/\        
 /_/\/ /_/\       
/__\_\/__\_\    


And here are triangles of height 3-7:

#3
        /\
       /_/\
      /__\_\
     /\ \__/\
    /_/\/ /_/\
   /__\_\/__\_\
  /\ \__/\ \__/\
 /_/\/ /_/\/ /_/\
/__\_\/__\_\/__\_\

#4
           /\
          /_/\
         /__\_\
        /\ \__/\
       /_/\/ /_/\
      /__\_\/__\_\
     /\ \__/\ \__/\
    /_/\/ /_/\/ /_/\
   /__\_\/__\_\/__\_\
  /\ \__/\ \__/\ \__/\
 /_/\/ /_/\/ /_/\/ /_/\
/__\_\/__\_\/__\_\/__\_\

#5
              /\
             /_/\
            /__\_\
           /\ \__/\
          /_/\/ /_/\
         /__\_\/__\_\
        /\ \__/\ \__/\
       /_/\/ /_/\/ /_/\
      /__\_\/__\_\/__\_\
     /\ \__/\ \__/\ \__/\
    /_/\/ /_/\/ /_/\/ /_/\
   /__\_\/__\_\/__\_\/__\_\
  /\ \__/\ \__/\ \__/\ \__/\
 /_/\/ /_/\/ /_/\/ /_/\/ /_/\
/__\_\/__\_\/__\_\/__\_\/__\_\

#6
                 /\
                /_/\
               /__\_\
              /\ \__/\
             /_/\/ /_/\
            /__\_\/__\_\
           /\ \__/\ \__/\
          /_/\/ /_/\/ /_/\
         /__\_\/__\_\/__\_\
        /\ \__/\ \__/\ \__/\
       /_/\/ /_/\/ /_/\/ /_/\
      /__\_\/__\_\/__\_\/__\_\
     /\ \__/\ \__/\ \__/\ \__/\
    /_/\/ /_/\/ /_/\/ /_/\/ /_/\
   /__\_\/__\_\/__\_\/__\_\/__\_\
  /\ \__/\ \__/\ \__/\ \__/\ \__/\
 /_/\/ /_/\/ /_/\/ /_/\/ /_/\/ /_/\
/__\_\/__\_\/__\_\/__\_\/__\_\/__\_\

#7
                    /\
                   /_/\
                  /__\_\
                 /\ \__/\
                /_/\/ /_/\
               /__\_\/__\_\
              /\ \__/\ \__/\
             /_/\/ /_/\/ /_/\
            /__\_\/__\_\/__\_\
           /\ \__/\ \__/\ \__/\
          /_/\/ /_/\/ /_/\/ /_/\
         /__\_\/__\_\/__\_\/__\_\
        /\ \__/\ \__/\ \__/\ \__/\
       /_/\/ /_/\/ /_/\/ /_/\/ /_/\
      /__\_\/__\_\/__\_\/__\_\/__\_\
     /\ \__/\ \__/\ \__/\ \__/\ \__/\
    /_/\/ /_/\/ /_/\/ /_/\/ /_/\/ /_/\
   /__\_\/__\_\/__\_\/__\_\/__\_\/__\_\
  /\ \__/\ \__/\ \__/\ \__/\ \__/\ \__/\
 /_/\/ /_/\/ /_/\/ /_/\/ /_/\/ /_/\/ /_/\
/__\_\/__\_\/__\_\/__\_\/__\_\/__\_\/__\_\


The Challenge

Write a program or function that takes a number n and prints a triangle-less triangle of height n. Trailing spaces on each line is acceptable, and up to one trailing or leading newline is also acceptable. IO can be in any reasonable format. The input is guarenteed to be a positive integer, so you don't have to worry about negative numbers, decimals, non-numbers etc.

Shortest answer in bytes wins!
Ruby, 79
-&gt;n{1.upto(n*=3){|i|puts (' '*(n-i)).ljust(n+i,'/__\_\/\ \__/_/\/ '[i%3*6,6])}}

A. (-4 bytes, -1 +1) changed from 0-indexed (.times) to 1-indexed (1.upto)
B. (-5 bytes) changed from array of three 6-char strings to selection of 6-char substring of 18-char string.
C. (-1 byte) m=n*3 -&gt; n*=3
D. (-5 bytes) reduced all five double backslashes to single backslashes (partly made possible by reordering of string required for point A)
Ruby, 94
-&gt;n{(m=n*3).times{|i|puts (' '*(m-i-1)).ljust(m+i+1,[ '/\\ \\__','/_/\\/ ','/__\\_\\'][i%3])}}

explanation
The basic unit is a 3x6 diamond as follows (last character on each row duplicated for clarity:)
    /\ \__/
   /_/\/ / 
  /__\_\/

All we need to do is display a suitable window of this pattern. Ruby's ljust allows you to pad with any string, not just spaces. Normally ljust would be used to pad a string of printable characters by adding spaces at the end, but here we use it in reverse: to pad a string of spaces by adding printable characters at the end.
ungolfed in test program
f=-&gt;n{
  (m=n*3).times{|i|                  #for each line of the triangle
    puts (' '*(m-i-1)).              #print m-i-1 spaces, 
      ljust(m+i+1,[ '/\\ \\__',      #left justified and padded to total length m+i+1
                   '/_/\\/ ',        #by one of these three strings
                  '/__\\_\\'][i%3])
  }
}

f[gets.to_i]