The 
th
truncated octahedral number, for a positive integer 
, is a figurate number
constructed from the 
th octahedral number
by removing the 
th square pyramid from
each of its six vertices,
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the 
th
octahedral number, 
is the 
th square pyramidal number,
and 
. The first few are 1, 38, 201, 586, ... (OEIS
A005910). The generating
function for the truncated octahedral numbers is
 |
(3)
|
for 
.
