A211798 -id:A211798 - 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

A211792 a(n) = Sum_{y=1..n} Sum_{x=1..n} floor((x^k + y^k)^(1/k)) with k = 3.

Original entry on oeis.org

1, 7, 22, 51, 97, 164, 258, 382, 541, 741, 982, 1271, 1611, 2008, 2466, 2986, 3577, 4241, 4982, 5807, 6715, 7714, 8808, 10000, 11297, 12701, 14217, 15848, 17600, 19477, 21482, 23620, 25895, 28313, 30879, 33592, 36460, 39487, 42678, 46036

Offset: 1

Clark Kimberling, Apr 26 2012

nonn

Row 3 of A211798.

			For a(3) we get the floor() values (1+2+3) + (2+2+3) + (3+3+3) = 22.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A211791, 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}]]

first(n) = { res = vector(n); res[1] = 1; for(i = 2, n, i3 = i^3; s = sum(j = 1, i-1, sqrtnint(i3 + j^3, 3)); res[i] = res[i-1] + sqrtnint(2*i3, 3) + 2*s; ); res } \\ David A. Corneth, Sep 12 2022

a(n) = Sum_{y=1..n} Sum_{x=1..n} floor((x^3 + y^3)^(1/3)).

a(n) = a(n-1) + floor((2*n^3)^(1/3)) + 2*Sum_{i = 1..n-1} floor((n^3 + i^3)^(1/3)) for n >= 2 and a(1) = 1. - David A. Corneth, Sep 12 2022

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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