Ten balls are stacked in a triangular array with 1 atop 2 atop 3 atop 4. (think of billiards.) the triangular array is free to rotate. find the generating function for the number of nonequivalent colorings with the colors red and blue. find the generating function if we are also allowed to turn over the array.

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.