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 A211808 Rectangular array:  R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^k<=x^k+y
 1, 5, 1, 16, 5, 1, 36, 16, 5, 1, 69, 36, 16, 5, 1, 117, 69, 38, 16, 5, 1, 184, 119, 73, 38, 16, 5, 1, 272, 190, 123, 75, 38, 16, 5, 1, 385, 282, 194, 131, 75, 38, 16, 5, 1, 525, 399, 290, 204, 131, 75, 38, 16, 5, 1, 696, 547, 415, 300, 210, 131, 75, 38, 16, 5, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row 1:  A055232 Row 2:  A211806 Row 3:  A211807 Limiting row sequence: A000330 Let R be the array in A211808 and let R' be the array in A182259.  Then R(k,n)+R'(k,n)=3^(n-1). See the Comments at A211790. LINKS EXAMPLE Northwest corner: 1...5...16...36...69...117...184 1...5...16...36...69...119...190 1...5...16...38...73...123...194 1...5...16...38...75...131...204 1...5...16...38...75...131...210 MATHEMATICA 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}]  (* A211806 *) Table[t[3, n], {n, 1, z}]  (* A211807 *) TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]] Flatten[Table[t[k, n - k + 1],      {n, 1, 12}, {k, 1, n}]] (* A211808 *) Table[k (4 k^2 - 3 k + 5)/6,      {k, 1, z}] (* row-limit sequence, A174723 *) (* Peter J. C. Moses, Apr 13 2012 *) CROSSREFS Cf. A211790. Sequence in context: A019429 A221364 A211805 * A093826 A144699 A066787 Adjacent sequences:  A211805 A211806 A211807 * A211809 A211810 A211811 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Apr 22 2012 STATUS approved

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Last modified April 16 00:05 EDT 2021. Contains 343020 sequences. (Running on oeis4.)