Rhombic Dodecahedral Number
Definition
A figurate number which is constructed as a centered cube with a square pyramid appended to each face, RhoDod_n | = | CCub_n + 6P_(n - 1)^(4) | = | (2n - 1)(2n^2 - 2n + 1), where CCub_n is a centered cube number and P_n^(4) is a square pyramidal number. The first few are 1, 15, 65, 175, 369, 671, ... (OEIS A005917). The generating function of the rhombic dodecahedral numbers is (x(x + 1)(x^2 + 10x + 1))/(x - 1)^4 = x + 15x^2 + 65x^3 + 175x^4 + ....
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