OFFSET
1,1
FORMULA
R(k,n) = Sum_{y=1..n} Sum_{x=1..n} floor((x^k + y^k)^(1/k)).
EXAMPLE
Northwest corner:
2 12 36 80 150 252 392
1 7 23 54 103 175 276
1 7 22 51 97 164 258
1 7 22 50 95 162 254
1 7 22 50 95 161 254
1 7 22 50 95 161 253
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Apr 26 2012
EXTENSIONS
Definition changed by Georg Fischer, Sep 10 2022
STATUS
approved