The 
th
truncated tetrahedral number, for a positive integer 
, is a figurate number
constructed by taking the 
th tetrahedral number
and removing the 
th tetrahedral number
from each of its four corners,
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the 
th
tetrahedral number and 
. The first few are 1, 16, 68, 180, 375, ... (OEIS
A005906). The generating
function for the truncated tetrahedral numbers is
 |
(3)
|
for 
.
