Centered octahedral number

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A centered octahedral number is a centered figurate number that represents an octahedron. The centered octahedral number for a specific n is given by

(2n+1)\times(2n^2+2n+3)\over 3

The first such numbers are 1, 7, 25, 63, 129, 231, 377, 575, 833, 1159, … (sequence A001845 in OEIS).

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