A figurate number constructed by taking the th tetrahedral number and removing the th tetrahedral number from each of the four corners,
The first few are 1, 16, 68, 180, 375, ... (OEIS A005906). The generating function for the truncated tetrahedral numbers is
More things to try:
Weisstein, Eric W. "Truncated Tetrahedral Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TruncatedTetrahedralNumber.html