Number of integer points in the 4-dimensional sliver in the n x n x n x n 4-cube.
1, 2, 6, 12, 23, 41, 70, 106, 159, 230, 323, 436, 578, 757, 975, 1232, 1536, 1889, 2317, 2797, 3355, 3994, 4711, 5523, 6438, 7465, 8618, 9888, 11296, 12839, 14557, 16398, 18449, 20689, 23115, 25758, 28591, 31673, 34995, 38586, 42415, 46528, 50984, 55687, 60739
0
The sliver is 0 <= x <= n, 0 <= y <= x, 0 <= z <= y, and 0 <= u <= z.
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 + d^2, {a, 0, nn}, {b, 0, a}, {c, 0, b}, {d, 0, c}]]], # <= nn^2 &]; Table[Length[Select[t, # <= n^2 &]], {n, 0, nn}]
Cf. A036702, S000691, S000693.
nonn
T. D. Noe, Jul 24 2015