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Truncated Tetrahedral Number

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A figurate number constructed by taking the (3n-2)th tetrahedral number and removing the (n-1)th tetrahedral number from each of the four corners,

Ttet_n=Te_(3n-3)-4Te_(n-1)
(1)
=1/6n(23n^2-27n+10).
(2)

The first few are 1, 16, 68, 180, 375, ... (OEIS A005906). The generating function for the truncated tetrahedral numbers is

(x(10x^2+12x+1))/((x-1)^4)=x+16x^2+68x^3+180x^4+....
(3)

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References

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 46-47, 1996.Sloane, N. J. A. Sequence A005906/M5002 in "The On-Line Encyclopedia of Integer Sequences."

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Truncated Tetrahedral Number

Cite this as:

Weisstein, Eric W. "Truncated Tetrahedral Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TruncatedTetrahedralNumber.html

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