A tetrahedral number, or triangular pyramidal number, or Digonal Deltahedral number is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The -th tetrahedral number is the sum of the first triangular numbers added up. The first few tetrahedral numbers (sequence A000292 in OEIS) are: 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, … The formula for the -th tetrahedral number is represented by the 3rd Rising Factorial divided by the 3rd Factorial. proof {| | | |- | | |- | | |} An observation of tetrahedral numbers: