A211792 -id:A211792 - cp's OEIS frontend

A211791 a(n) = Sum_{y=1..n} Sum_{x=1..n} floor((x^k + y^k)^(1/k)) with k = 2.

1, 7, 23, 54, 103, 175, 276, 409, 579, 791, 1050, 1360, 1724, 2149, 2640, 3198, 3832, 4543, 5337, 6217, 7192, 8265, 9437, 10716, 12103, 13609, 15231, 16978, 18857, 20869, 23018, 25307, 27745, 30337, 33084, 35992, 39066, 42309, 45728

Offset: 1

Clark Kimberling, Apr 26 2012

nonn

Row 2 of A211798.

			For a(3) we get the floor() values (1+2+3) + (2+2+3) + (3+3+4) = 23.

Cf. A211792, A211798.

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}]]

a(n) = Sum_{y=1..n} Sum_{x=1..n} floor(sqrt(x^2 + y^2)).

Definition corrected by Georg Fischer, Sep 10 2022

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.

Original entry on oeis.org

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

Clark Kimberling, Apr 26 2012

			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

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

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}]]

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

Definition changed by Georg Fischer, Sep 10 2022

cp's OEIS Frontend

A211791 a(n) = Sum_{y=1..n} Sum_{x=1..n} floor((x^k + y^k)^(1/k)) with k = 2.

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