Smooth step sum of functions

This function is all operations in base 2 for ease of calculation on a computer...

h is the height and a is a point on the x-axis, like below for height for at a=3...

It's nearly flat on top, and at half a unit away in either direction it is one quarter of the full height, which makes it so when you put it next to another function of the same type, the point halfway between them is halfway between the height of both... There is negligible height anywhere outside of [a-1...a+1]

the leading coefficients in the above are 2,5,-1,3,2,5 so those are the heights for a = 0,1,2,3,4,5