What method of numerical integration is this? I am trying to update some old code that finds the area under a curve from $17$ evenly spaced discrete data points. I'd like to update it to calculate from $65$ data points. I'd like to use the same methodology, so I'm trying to determine the method used to approximate it. The code looks like this:
$$
\begin{align}
Area = \frac{20\cdot 10^{-9}}{3}\cdot &(Data(0)+Data(16) + Data(1)\cdot2 + Data(2)\cdot 4\\ &+ Data(3)\cdot 2 +Data(4)\cdot4+ \cdots +Data(15)\cdot2)
\end{align}
$$
The $ 20\cdot 10^{-9} $ comes from the $x$-axis spacing between points, but I'm having trouble understanding why they alternate between multiplying by $2$ and $4$ in the summation. Does anyone have an idea what type of approximation follows a pattern like this?

This appears to be the composite Simpson rule: https://en.wikipedia.org/wiki/Simpson%27s_rule#Composite_Simpson.27s_rule 
A summary: start with a partition of $[a,b]$ into $N$ subintervals of equal length, and add a point in the middle of each of the subintervals. Now you have $2N+1$ evaluation points. (Note that this is always odd, regardless of whether $N$ was even or odd.)
On each of the original $N$ subintervals, you take a quadratic interpolant through the three evaluation points, integrate that interpolant. Then you sum over the intervals. On each subinterval, the weights arising from integrating the interpolant turn out to be $1,4,1$. (There is nothing special going on here, it's just a calculation.) But the endpoints of the subintervals other than the first and last one get used twice (as the left endpoint of one interval and the right endpoint of another), so they get double counted, which is where the $2$s come from.
