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

1,1

Links

Table of n, a(n) for n=1..64.

Formula

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

Example

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

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}]]

Crossrefs

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

Sequence in context: A113491 A107773 A221075 * A075180 A227830 A299521

Adjacent sequences: A211795 A211796 A211797 * A211799 A211800 A211801

Keyword

nonn,tabl

Author

Clark Kimberling, Apr 26 2012

Extensions

Definition changed by Georg Fischer, Sep 10 2022

Status

approved