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Truncated Tetrahedral Number

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,

{\rm Ttet}_n\equiv {\rm Te}_{3n-3}-4{\rm Te}_{n-1}={\textstyle{1\over 6}} n(23n^2-27n+10).

The first few are 1, 16, 68, 180, 375, ... (Sloane's A005906). The Generating Function for the truncated tetrahedral numbers is



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 ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein