A figurate number which is constructed as an octahedral number with a square pyramid removed from each of the six graph vertices, TO_n | = | O_(3n - 2) - 6P_(n - 1)^(4) | = | 16n^3 - 33n^2 + 24n - 6, where O_n is an octahedral number and P_n^(4) is a square pyramidal number. The first few are 1, 38, 201, 586, ... (OEIS A005910). The generating function for the truncated octahedral numbers is (x(6x^3 + 55x^2 + 34x + 1))/(x - 1)^4 = x + 38x^2 + 201x^3 + ....

octahedral number | square pyramidal number