A figurate number constructed by taking the 
th tetrahedral number and removing the 
th tetrahedral number from each of the four corners,
th tetrahedral number and removing the th tetrahedral number from each of the four corners, |  |  |
(1)
|
 |  |  |
(2)
|
The first few are 1, 16, 68, 180, 375, ... (Sloane's A005906). The generating function for the truncated tetrahedral numbers is
 (3) |
Ref: mathworld.wolfram.com
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