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Truncated triangular pyramid number

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Truncated Triangular Pyramid Number[1] are achieved by removing (truncating) some smaller Tetrahedral number (or triangular pyramidal number) from each of the vertices of a bigger Tetrahedral number (or triangular pyramidal number).

A pyramid with side length 5 contains 35 spheres. Each layer represents one of the first five triangular numbers.

The number to be removed (truncated) may be same or different from the different vertices and works for only specific Tetrahedral number (or triangular pyramidal number).

For example,

Tetrahedral Number 20 (sequence A000292 in the OEIS) yields Truncated Triangular Pyramid Number 7 (sequence A051937 in the OEIS) by truncating Tetrahedral number (or triangular pyramidal number) 4,4,4 and 1 from its vertices

Tetrahedral Number 35 (sequence A000292 in the OEIS) yields Truncated Triangular Pyramid Number 19 (sequence A051937 in the OEIS) by truncating Tetrahedral number (or triangular pyramidal number) 4 from each of the vertices

Tetrahedral Number 286 (sequence A000292 in the OEIS) yields Truncated Triangular Pyramid Number 273 (sequence A051937 in the OEIS) by truncating Tetrahedral number (or triangular pyramidal number) 4,4,4 and 1 from its vertices

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A051937 (Truncated triangular pyramid numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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