Build a triangle without any triangles
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]