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).

References

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