Going down the diagonals produces a constant sequence of 1's, the natural numbers, the triangular numbers, the tetrahedral numbers, and so on for n-simplex numbers.
Going up slants (for example, in this image by starting on a hexagon on left border facing the upper-right vertex and crossing edges and hexagons) and summing produces the Fibonacci numbers.
>>13338877Was veritasium the one who had a video about the fractions "between" the integer entries? I actually think that explanation is neat, as is the use of the binomial theorem for algebraic extensions.
>>13338929Elementary consequence of the binomial theorem, as is this:
Concatenating the entries of the first 4 rows yields the first four powers of 11 (1, 11, 121, 1331, 14641). For higher powers, multiple-digit numbers must be aligned properly (i.e., [1, 5 + 1, 0 + 1, 0, 5, 1] => 11^5 = 161051)
