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Let's experiment.

Figure 9. The first modification of Pascal's Triangle.

If we replace ones in the first column  with twos and build the 2nd, 3rd, and 4th columns according to the fundamental rule, we will see:

Odd numbers (n), - (the sign is chosen because of its similarity to the gnomon),

Square numbers (n) ,

Pyramidal (square pyramid) number (n). 

In Fibonacci lines in one direction there are series with a slightly changed beginning: Fibonacci numbers (2, 2, 3, 5, 8...) and Lucas* numbers (2, 1, 3, 4, 7, 11, 19...) (are formed according to the Fibonacci numbers rule ).

* French mathematician Edouard Lucas, the 19th century.


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