(0,0) (1,1) (2,7) (3,19) (4,37)
What function is best described the sequence
differences: 1 6 12 18
∑6k = 3k(k+1)/2
So, except for the (0,0) term, it looks like a quadratic, where
f(0) = 0
f(x) = 1+3x(x-1) for x>0
Maybe you can resolve the typo?