Explaining Concept-Tiers

I recently created the term 'concept tiers' to show pattern recognition. I will use number series as an example to explain.

1,4,8,13,19

the difference between the numbers in the above sequence is:

3,4,5,6

The resulting sequence as show above is defined as a pattern. Now the pattern itself has a pattern:

1,1,1,1. This is defined as tier 1 concept. That is, pattern of a pattern is a tier 1 concept. Pattern of a pattern of a pattern is a tier 2 concept.

(I wonder if you can have a series not just going left to right but all over the paper like a matrix. But that would be a matrix.).

Now that gives me an idea:

'Sayam's Conjecture':

All positively growing sequences can be generated by starting with 1, 1, 1,,1 etc.