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Tetrahedral numbers

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Tetrahedral numbers or triangular pyramidal numbers are 3-dimensional figurate numbers representing tetrahedra (or tetrahedrons). The th tetrahedral number is given by the formula

with being the th triangular number.

Tetrahedral numbers can also be obtained from binomial coefficients (which means that they can be looked up in Pascal's triangle)

where is the rising factorial.

A000292 Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.

{0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, ...}

See also