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An octahedral number is a figurate number that represents an octahedron, or two pyramids placed together, one upside-down underneath the other. The octahedral number for n can be obtained by adding the n-1 and n square pyramidal numbers together, or by using the following formula:
<math>{1 \over 3}n(2n^2 + 1)<math>
The first few octahedral numbers are
1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891
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