A figurate number corresponding to a configuration of points which form a pyramid with r-sided regular polygon bases can be thought of as a generalized pyramidal number, and has the form P_n^(r) = 1/6 n(n + 1)[(r - 2) n + (5 - r)]. The first few cases are therefore P_n^(3) | = | 1/6 n(n + 1)(n + 2) P_n^(4) | = | 1/6 n(n + 1)(2n + 1) P_n^(5) | = | 1/2 n^2(n + 1), so r = 3 corresponds to a tetrahedral number T e_n, and r = 4 to a square pyramidal number P_n.
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