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Truncated Octahedral Number

A Figurate Number which is constructed as an Octahedral Number with a Square Pyramid removed from each of the six Vertices,

{\it TO}_n=O_{3n-2}-6P_{n-1}={\textstyle{1\over 3}}(3n-2)[2(3n-2)^2+1],

where $O_n$ is an Octahedral Number and $P_n$ is a Pyramidal Number. The first few are 1, 38, 201, 586, ... (Sloane's A005910). The Generating Function for the truncated octahedral numbers is


See also Octahedral Number


Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, p. 52, 1996.

Sloane, N. J. A. Sequence A005910/M5266 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