Another relationship involves the Pascal Triangle : Whereas the classical Pascal Triangle with sides has diagonals with the natural numbers, triangular numbers, and tetrahedral numbers, generating the Fibonacci numbers as sums of samplings across diagonals, the sister Pascal with sides has equivalent diagonals with odd numbers, square numbers, and square pyramidal numbers, respectively, and generates ( by the same procedure ) the Lucas numbers rather than Fibonacci.
12.
Furthermore, the entries of this triangle can be computed from Pascal's, " the terms in each row are the initial term divided by the corresponding Pascal triangle entries . " In fact, each diagonal relates to corresponding Pascal Triangle diagonals : The first Leibniz diagonal consists of 1 / ( 1x natural numbers ), the second of 1 / ( 2x triangular numbers ), the third of 1 / ( 3x tetrahedral numbers ) and so on.
13.
Furthermore, the entries of this triangle can be computed from Pascal's, " the terms in each row are the initial term divided by the corresponding Pascal triangle entries . " In fact, each diagonal relates to corresponding Pascal Triangle diagonals : The first Leibniz diagonal consists of 1 / ( 1x natural numbers ), the second of 1 / ( 2x triangular numbers ), the third of 1 / ( 3x tetrahedral numbers ) and so on.
