Binary Images of Triangle Counts
Mathematica, 126 122 121 89 bytes

Image[1-Thread@IntegerDigits[l=Round[(#+3#~Mod~2)^2/48]&amp;/@Range@##,2,⌈2~Log~Max@l⌉]]&amp;


This defines an unnamed function taking the two integers as parameters and displaying the image on screen. It plots each square as a single pixel, but if you like you can actually zoom in.

I'm now using an explicit formula given in the OEIS article (first one in the Mathematica section, thanks to David Carraher for pointing that out). It's also blazingly fast now.

Here is the indented code with a few comments:

Image[1-Thread@IntegerDigits[   (* 3. Convert each number to padded binary, transpose
                                      invert colours, and render as Image. *)
    l = Round[
      (#+3#~Mod~2)^2/48
    ] &amp; /@ Range@##,            (* 1. Turn input into a range and get the Alcuin
                                      number for each element. *)
    2,
    ⌈2~Log~Max@l⌉               (* 2. Determine the maximum number of binary digits. *)
]] &amp;


Here is the output for 0, 600: