For ten points, identify this object in which every number is the sum of the two numbers above it.
The Lucas correspondence relates the Hanoi graph to a graph derived from this object. One early reference to this object called it the Staircase of Mount Meru, and in some countries, this object is alternately named for Yang Hui or   Khayyam. If part of this object is represented as a matrix, the determinant of that matrix will be 1. The diagonals of this object contain the  gurate numbers of simplices with progressively higher dimension; this notably includes the tri- angular numbers. This object's entries correspond to coe cients of binomials. For ten points, identify this object in which every number is the sum of the two numbers above it.
The Lucas correspondence relates the Hanoi graph to a graph derived from this object.
Pascal's triangle [accept Yang Hui's triangle and Khayyam's triangle before their respective mentions]