Centered tetrahedral number

A centered tetrahedral number is a centered figurate number that represents a tetrahedron. That is, it counts the dots in a three-dimensional dot pattern with a single dot surrounded by tetrahedral shells.[1] The th centered tetrahedral number, starting at for a single dot, is:[2][3]

Centered tetrahedral number
Total no. of termsInfinity
Subsequence ofPolyhedral numbers
Formula
First terms1, 5, 15, 35, 69, 121, 195
OEIS index

The first such numbers are:[1][2]

1, 5, 15, 35, 69, 121, 195, 295, 425, 589, 791, ...

References

edit
  1. ^ a b Deza, E.; Deza, M. (2012). Figurate Numbers. Singapore: World Scientific Publishing. pp. 126–128. ISBN 978-981-4355-48-3.
  2. ^ a b Sloane, N. J. A. (ed.). "Sequence A005894 (Centered tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Deza numbers the centered tetrahedral numbers at   for a single dot, leading to a different formula.