In the normal summation, we can do this:
And that would sum a list X as such in Python:
>>> x = [1,2,3,4]
>>> sum([x_i for i,x_i in enumerate(x)])
10
Is there a mathematical symbol for pairwise sum? Like summing the first and second, then second and third, then third and forth? In Python:
>>> from itertools import tee, izip
>>> def pairwise(iterable):
... "s -> (s0,s1), (s1,s2), (s2, s3), ..."
... a, b = tee(iterable)
... next(b, None)
... return zip(a, b)
...
>>> x = [1,2,3,4]
>>> sum([x_i*x_j for x_i,x_j in pairwise(x)])
20
Would this math formulation be correct?
But there's a strange case in the formula above where i==n and i+1 doesn't exist.