A centered tetrahedral number is a centered
figurate number
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean
* polygon ...
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 o ...
. 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
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