A166190 Number of 4 X 4 X 4 triangular nonnegative integer arrays with all sums of an element and its neighbors <= n.

1, 21, 207, 1298, 6052, 22824, 73383, 208269, 534687, 1264026, 2788834, 5802288, 11477240, 21726484, 39571482, 69652946, 118924069, 197575191, 320248137, 507608530, 788356140, 1201765708, 1800865001, 2656371783, 3861528515