login
a(n) = Sum_{y=1..n} Sum_{x=1..n} floor((x^k + y^k)^(1/k)) with k = 2.
3

%I #15 Sep 11 2022 00:44:41

%S 1,7,23,54,103,175,276,409,579,791,1050,1360,1724,2149,2640,3198,3832,

%T 4543,5337,6217,7192,8265,9437,10716,12103,13609,15231,16978,18857,

%U 20869,23018,25307,27745,30337,33084,35992,39066,42309,45728

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

%C Row 2 of A211798.

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

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

%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. A211792, A211798.

%K nonn

%O 1,2

%A _Clark Kimberling_, Apr 26 2012

%E Definition corrected by _Georg Fischer_, Sep 10 2022