honestly i don't remember it was written in my statistics class at 9am
i'm also partially curious as to why the program works, i know what its doing, i worked it out by hand before writing it in perl
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A simple explanation of why it works, since you wondered:
If you continue your triangle, you end up with this:
1
1 1
1 0 1
1 1 1 1
1 0 0 0 1
1 1 0 0 1 1
1 0 1 0 1 0 1
1 1 1 1 1 1 1 1
1 0 0 0 0 0 0 0 1
1 1 0 0 0 0 0 0 1 1
1 0 1 0 0 0 0 0 1 0 1
1 1 1 1 0 0 0 0 1 1 1 1
1 0 0 0 1 0 0 0 1 0 0 0 1
1 1 0 0 1 1 0 0 1 1 0 0 1 1
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
You probably see a pattern by now, but if not, change all the 0s to spaces, and all the 1s to #s:
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
# #
# # # #
# # # #
# # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #
No matter how far down you go, you always end up with a triangle, and you can continue by copying that triangle to its bottom left and right sides. This is easy to see, but I can't find the words that actually explain it, so please take a look for yourself if you have doubts about that. Now take a look at this: the first row has 1 as its sum. This triangle-point is copied twice, so the first 2 * 1 rows have 3 * 1 as their sum. This triangle is copied twice, so the first 2 * 2 * 1 rows have 3 * 3 * 1 as their sum. The first 2^3 * 1 rows have 3^3 * 1 as their sum. I'm sure you get the idea by now :)
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