Is this sequence significant? I'm doing some algorithmic work and stumbled onto a strange pattern.  Does anyone know if this is some common thing? (like does this converge towards the gaussian curve perhaps??)
starting with:
1,3,3,1
I offset it to the right one value and add it to itself
1,3+1,3+3,1+3,1=
1,4,6,4,1
continuing that same algorithm it then spits out this:
1,5,10,10,5,1
then:
1,6,15,20,15,6,1
then:
1,7,21,35,35,21,7,1
then:
1,8,28,56,70,56,28,8,1
Look familiar to anyone, or anyone see what the pattern is converging on?
Here's a link to the last set of values, plotted in wolfram alpha
http://www.wolframalpha.com/input/?i=plot+1%2C8%2C28%2C56%2C70%2C56%2C28%2C8%2C1
Thanks!!

What you're describing is Pascal's Triangle.
http://en.wikipedia.org/wiki/Pascal%27s_triangle
