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A211802
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R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and 2*w^k < x^k + y^k; square array read by descending diagonals.
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6
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0, 3, 0, 11, 3, 0, 28, 13, 3, 0, 56, 32, 13, 3, 0, 99, 64, 34, 13, 3, 0, 159, 113, 68, 34, 13, 3, 0, 240, 181, 117, 70, 34, 13, 3, 0, 344, 272, 187, 125, 70, 34, 13, 3, 0, 475, 388, 282, 197, 125, 70, 34, 13, 3, 0, 635, 535, 406, 292, 203, 125, 70, 34, 13, 3, 0
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OFFSET
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1,2
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COMMENTS
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Let R be the array in this sequence and let R' be the array in A211805. Then R(k,n) + R'(k,n) = 3^(n-1).
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LINKS
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EXAMPLE
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Northwest corner:
0 3 11 28 56 99 159 240
0 3 13 32 64 113 181 272
0 3 13 34 68 117 187 282
0 3 13 34 70 125 197 292
0 3 13 34 70 125 203 302
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MATHEMATICA
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z = 48;
t[k_, n_] := Module[{s = 0},
(Do[If[2 w^k < x^k + y^k, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)];
Table[t[1, n], {n, 1, z}] (* A182260 *)
Table[t[2, n], {n, 1, z}] (* A211800 *)
Table[t[3, n], {n, 1, z}] (* A211801 *)
TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
Flatten[Table[t[k, n - k + 1], {n, 1, 12},
Table[k (k - 1) (4 k + 1)/6, {k, 1,
z}] (* row-limit sequence, A016061 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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