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.