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A211805
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Rectangular array: R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^k>=x^k+y<k.
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5
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1, 5, 1, 16, 5, 1, 36, 14, 5, 1, 69, 32, 14, 5, 1, 117, 61, 30, 14, 5, 1, 184, 103, 57, 30, 14, 5, 1, 272, 162, 99, 55, 30, 14, 5, 1, 385, 240, 156, 91, 55, 30, 14, 5, 1, 525, 341, 230, 146, 91, 55, 30, 14, 5, 1, 696, 465, 323, 220, 140, 91, 55, 30, 14, 5, 1, 900
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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 A211802 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:
1...5...16...36...69...117...184
1...5...14...32...61...103...162
1...5...14...30...57...99....156
1...5...14...30...55...91....146
1...5...14...30...55...91....140
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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}] (* A055232 *)
Table[t[2, n], {n, 1, z}] (* A211803 *)
Table[t[3, n], {n, 1, z}] (* A211804 *)
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) (2 k + 1)/6,
{k, 1, z}] (* row-limit sequence, A000330 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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