A centered tetrahedral number is a centered
figurate number that represents a
tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ...
. The centered tetrahedral number for a specific ''n'' is given by
The first such numbers are 1, 5, 15, 35, 69, 121, 195, 295, 425, 589, 791, ... .
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
*
Figurate numbers
{{Num-stub