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 
.
