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.

%I A211791 #15 Sep 11 2022 00:44:41
%S A211791 1,7,23,54,103,175,276,409,579,791,1050,1360,1724,2149,2640,3198,3832,
%T A211791 4543,5337,6217,7192,8265,9437,10716,12103,13609,15231,16978,18857,
%U A211791 20869,23018,25307,27745,30337,33084,35992,39066,42309,45728
%N A211791 a(n) = Sum_{y=1..n} Sum_{x=1..n} floor((x^k + y^k)^(1/k)) with k = 2.
%C A211791 Row 2 of A211798.
%F A211791 a(n) = Sum_{y=1..n} Sum_{x=1..n} floor(sqrt(x^2 + y^2)).
%e A211791 For a(3) we get the floor() values (1+2+3) + (2+2+3) + (3+3+4) = 23.
%t A211791 f[x_, y_, k_] := f[x, y, k] = Floor[(x^k + y^k)^(1/k)]
%t A211791 t[k_, n_] := Sum[Sum[f[x, y, k], {x, 1, n}], {y, 1, n}]
%t A211791 Table[t[1, n], {n, 1, 45}]  (* 2*A002411 *)
%t A211791 Table[t[2, n], {n, 1, 45}]  (* A211791 *)
%t A211791 Table[t[3, n], {n, 1, 45}]  (* A211792 *)
%t A211791 TableForm[Table[t[k, n], {k, 1, 12},
%t A211791                  {n, 1, 16}]] (* A211798 *)
%t A211791 Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]]
%Y A211791 Cf. A211792, A211798.
%K A211791 nonn
%O A211791 1,2
%A A211791 _Clark Kimberling_, Apr 26 2012
%E A211791 Definition corrected by _Georg Fischer_, Sep 10 2022