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

1,2

Comments

Row 2 of A211798.

Links

Table of n, a(n) for n=1..39.

Formula

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

Example

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

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. A211792, A211798.

Sequence in context: A038796 A332492 A304724 * A004068 A261893 A022815

Adjacent sequences: A211788 A211789 A211790 * A211792 A211793 A211794

Keyword

nonn

Author

Clark Kimberling, Apr 26 2012

Extensions

Definition corrected by Georg Fischer, Sep 10 2022

Status

approved