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A211798
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R(k,n) = Sum_{y=1..n} Sum_{x=1..n} floor((x^k + y^k)^(1/k)), square array read by descending antidiagonals.
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3
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2, 12, 1, 36, 7, 1, 80, 23, 7, 1, 150, 54, 22, 7, 1, 252, 103, 51, 22, 7, 1, 392, 175, 97, 50, 22, 7, 1, 576, 276, 164, 95, 50, 22, 7, 1, 810, 409, 258, 162, 95, 50, 22, 7, 1, 1100, 579, 382, 254, 161, 95, 50, 22, 7, 1, 1452, 791, 541, 375, 253, 161, 95, 50, 22
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..64.
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FORMULA
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R(k,n) = Sum_{y=1..n} Sum_{x=1..n} floor((x^k + y^k)^(1/k)).
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EXAMPLE
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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
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MATHEMATICA
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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}]]
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CROSSREFS
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Cf. A002411 ((1/2) * row 1), A002412 (limiting row), A211791 (row 2), A211792 (row 3).
Sequence in context: A113491 A107773 A221075 * A075180 A227830 A299521
Adjacent sequences: A211795 A211796 A211797 * A211799 A211800 A211801
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Apr 26 2012
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EXTENSIONS
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Definition changed by Georg Fischer, Sep 10 2022
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STATUS
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approved
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