Centered tetrahedral number

A centered tetrahedral number is a centered figurate number that represents a tetrahedron. The centered tetrahedral number for a specific n is given by

$(2n+1)\times {(n^{2}+n+3) \over 3}$

The first such numbers are 1, 5, 15, 35, 69, 121, 195, 295, 425, 589, 791, ... (sequence A005894 in the OEIS).

Parity And divisibility

Every centered tetrahedral number is odd.
Every centered tetrahedral number with an index of 2,3 or 4 Modulo 5 is divisible by 5.

References

Deza, E.; Deza, M. (2012). Figurate Numbers. Singapore: World Scientific Publishing. pp. 126–128. ISBN 978-981-4355-48-3.

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