A211798 R(k,n) = Sum_{y=1..n} Sum_{x=1..n} floor((x^k + y^k)^(1/k)), square array read by descending antidiagonals.

2, 12, 1, 36, 7, 1, 80, 23, 7, 1, 150, 54, 22, 7, 1, 252, 103, 51, 22, 7, 1, 392, 175, 97, 50, 22, 7, 1, 576, 276, 164, 95, 50, 22, 7, 1, 810, 409, 258, 162, 95, 50, 22, 7, 1, 1100, 579, 382, 254, 161, 95, 50, 22, 7, 1, 1452, 791, 541, 375, 253, 161, 95, 50, 22

Offset: 1

Author

Clark Kimberling, Apr 26 2012

Keywords

• nonn
• tabl

Examples

			Northwest corner:
  2  12  36  80 150 252 392
  1   7  23  54 103 175 276
  1   7  22  51  97 164 258
  1   7  22  50  95 162 254
  1   7  22  50  95 161 254
  1   7  22  50  95 161 253
		

Crossrefs

Cf. A002411 ((1/2) * row 1), A002412 (limiting row), A211791 (row 2), A211792 (row 3).

Programs

Mathematica

f[x_, y_, k_] := f[x, y, k] = Floor[(x^k + y^k)^(1/k)]
t[k_, n_] := Sum[Sum[f[x, y, k], {x, 1, n}], {y, 1, n}]
Table[t[1, n], {n, 1, 45}]  (* 2*A002411 *)
Table[t[2, n], {n, 1, 45}]  (* A211791 *)
Table[t[3, n], {n, 1, 45}]  (* A211792 *)
TableForm[Table[t[k, n], {k, 1, 12},
                 {n, 1, 16}]] (* A211798 *)
Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]]

Formula

R(k,n) = Sum_{y=1..n} Sum_{x=1..n} floor((x^k + y^k)^(1/k)).

Extensions

Definition changed by Georg Fischer, Sep 10 2022