Infinite triangular arrays

Infinite triangular arrays consist of symmetric triangles composed of numbers with each lower row computed from the values of the row above. The most famous example is Pascal's triangle wherein the sum of two adjacent numbers in a row gives the number in the row beneath. Another example is Dudley's triangle which was suggested in 1987. Another example is Pascal's pyramid which is the three dimensional version of Pascal's triangle. Patterns emerge on these arrays when specific values are highlighted, such as only even numbers or prime numbers.