tetrahedral number

Noun

 * 1)  A number which results from the summation of consecutive triangular numbers, starting from 1. If the triangular numbers in such a summation are depicted as horizontal triangular arrays of units then these arrays can be stacked vertically to yield a tetrahedral array.
 * The $$n$$th tetrahedral number can be calculated with the formula $${(n + 1)^3 - (n + 1) \over 6}$$.