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Octahedral Number

A Figurate Number which is the sum of two consecutive Pyramidal Numbers,

O_n=P_{n-1}+P_n={\textstyle{1\over 3}} n(2n^2+1).

The first few are 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, 1156, ... (Sloane's A005900). The Generating Function for the octahedral numbers is


See also Truncated Octahedral Number


Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, p. 50, 1996.

Sloane, N. J. A. Sequence A005900/M4128 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