Number of integer points in the 3-dimensional sliver in the n x n x n cube.
1, 2, 5, 10, 16, 27, 42, 58, 80, 110, 143, 182, 226, 281, 343, 413, 489, 576, 676, 783, 901, 1035, 1172, 1328, 1493, 1674, 1872, 2086, 2308, 2544, 2805, 3069, 3364, 3679, 4000, 4348, 4709, 5096, 5493, 5926, 6366, 6832, 7330, 7841, 8380, 8950, 9528, 10134, 10766
0
The sliver is 0 <= x <= n, 0 <= y <= x, and 0 <= z <= y.
T. D. Noe, Plot of 201 terms
T. D. Noe, Table of 201 terms
(Mma) nn = 50; t = Select[Sort[Flatten[Table[a^2 + b^2 + c^2, {a, 0, nn}, {b, 0, a}, {c, 0, b}]]], # <= nn^2 &]; Table[Length[Select[t, # <= n^2 &]], {n, 0, nn}]
Cf. A036702, S000692, S000693.
nonn
T. D. Noe, Jul 24 2015