How can I find information of "difference tables"?

Hello everybody. Its about -15 degrees celsius here in north Europe.

I have high school mathematical level education...in university I have taken only some courses from statistics. So, mathematics is my dear hobby.

About 2-3 years ago I found to my surprise an easy method never taught to me at school (well, it was some 20 years ago when I was at school...). Below there is a short example of it:

4^0 = 1

4^1 = 4

4^2 = 16

4^3 = 64

...

So, at the beginning we have base number four and it is raised to consecutive integer powers.
After that we subtract them pair by pair like that:

1
4 - 1 = 3
4
16 - 4 = 12
16
64 - 16 = 48
64

...

After that we continue the same theme...that is: pair by pair subtraction and get:

1
3
4 9
12 27
16 36
48
64

...
If we now look at upper diagonal, we can see, that there are natural number raisings of base number 3 (3^0=1 ; 3^1=3 ; 3^2=9 and 3^3=27...).
If, on the other hand, we had used summations instead of subtractions, there would be raisings of base number 5 instead.

Since then I have found many modifications of this theme. However, it took some 20-30 popular science/math books before I encountered that same method from an other source (It was John H Conway & Richard K Guys "The Book of Numbers", pages 79-89, 1996). They had named it "difference table".
Some findings consearning this method I cannot find from "The Book of Numbers" however, which explains why I present this problem here.

So, I have a practical problem: If I try to find more publications where this method has been used/analyzed, I write this "difference table" to Google or similar search engine. The problem is, that most of information it offears consearns calculus, derivations, differentiation etc. which I am now not so interested in. Actually I have the same problem with Math Help Forum too.

So:

1) Is there any other name for this method or search strategy I should use in order to find more information of it?
2) Does anyone already knows and recommends any useful source, web page, journal, book etc (which is, well, understandable, to a person who has high school math education only) of this subject?
3) As this is an easy and useful method (I think), I was quite surprised and disappointed when it was not taught to me at school! Here in Finland we had had two alternatives at high school: math oriented or foreign language oriented...and I had chosen the former one. So, perhaps you understand my disappointment. What kind is the situation now in Finland (if someone of readers comes from here)? Is this a method that is part of curriculum in other societies? I am just interested.