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A211802
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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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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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Row 1: A182260
Row 2: A211800
Row 3: A211801
Limiting row sequence: A016061
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).
See the Comments at A211790.
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LINKS
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Table of n, a(n) for n=1..66.
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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},
{k, 1, n}]] (* A211802 *)
Table[k (k - 1) (4 k + 1)/6, {k, 1,
z}] (* row-limit sequence, A016061 *)
(* Peter J. C. Moses, Apr 13 2012 *)
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CROSSREFS
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Cf. A211790.
Sequence in context: A252096 A216470 A182259 * A249775 A019264 A028851
Adjacent sequences: A211799 A211800 A211801 * A211803 A211804 A211805
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Apr 22 2012
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STATUS
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approved
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