A211798 - OEIS

%I #21 Sep 11 2022 00:45:33

%S 2,12,1,36,7,1,80,23,7,1,150,54,22,7,1,252,103,51,22,7,1,392,175,97,

%T 50,22,7,1,576,276,164,95,50,22,7,1,810,409,258,162,95,50,22,7,1,1100,

%U 579,382,254,161,95,50,22,7,1,1452,791,541,375,253,161,95,50,22

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

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

%e Northwest corner:

%e   2  12  36  80 150 252 392

%e   1   7  23  54 103 175 276

%e   1   7  22  51  97 164 258

%e   1   7  22  50  95 162 254

%e   1   7  22  50  95 161 254

%e   1   7  22  50  95 161 253

%t f[x_, y_, k_] := f[x, y, k] = Floor[(x^k + y^k)^(1/k)]

%t t[k_, n_] := Sum[Sum[f[x, y, k], {x, 1, n}], {y, 1, n}]

%t Table[t[1, n], {n, 1, 45}]  (* 2*A002411 *)

%t Table[t[2, n], {n, 1, 45}]  (* A211791 *)

%t Table[t[3, n], {n, 1, 45}]  (* A211792 *)

%t TableForm[Table[t[k, n], {k, 1, 12},

%t                  {n, 1, 16}]] (* A211798 *)

%t Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]]

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

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Apr 26 2012

%E Definition changed by _Georg Fischer_, Sep 10 2022