Work out tetrahedral number instantly with clear inputs, formula shown and shareable results.
Tetrahedral numbers stack triangular layers into a pyramid, giving Teₙ = n(n + 1)(n + 2)/6 — the running total of the triangular numbers. They also form the third diagonal of Pascal's triangle.
Tetrahedral number
Teₙ = n(n + 1)(n + 2) / 6 = C(n + 2, 3)
10 × 11 × 12 / 6 = 220, the number of cannonballs in a ten-layer pyramid.
Only 1, 4 and 19600 — a result proved in the 1870s.