Number of integer points in the 5-dimensional sliver in the n x n x n x n x n 5-cube.
1, 2, 6, 14, 29, 56, 101, 166, 267, 407, 604, 865, 1211, 1659, 2236, 2956, 3861, 4949, 6299, 7906, 9849, 12120, 14817, 17958, 21641, 25859, 30753, 36318, 42732, 49917, 58116, 67296, 77693, 89219, 102175, 116527, 132515, 150117, 169602, 191013, 214662, 240393
0
The sliver is 0 <= x <= n, 0 <= y <= x, 0 <= z <= y, 0 <= u <= z, and 0 <= v <= u.
T. D. Noe, Plot of 101 terms
T. D. Noe, Table of 101 terms
(Mma) nn = 40; t = Select[Sort[Flatten[Table[a^2 + b^2 + c^2 + d^2 + e^2, {a, 0, nn}, {b, 0, a}, {c, 0, b}, {d, 0, c}, {e, 0, d}]]], # <= nn^2 &]; Table[Length[Select[t, # <= n^2 &]], {n, 0, nn}]
Cf. A036702, S000691, S000692.
nonn
T. D. Noe, Jul 24 2015