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 A211799 Rectangular array:  R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and w^k<=x^k+y
 0, 0, 0, 1, 1, 0, 4, 5, 1, 0, 10, 13, 5, 1, 0, 20, 26, 14, 5, 1, 0, 35, 48, 29, 14, 5, 1, 0, 56, 78, 53, 30, 14, 5, 1, 0, 84, 119, 88, 55, 30, 14, 5, 1, 0, 120, 173, 134, 90, 55, 30, 14, 5, 1, 0, 165, 240, 195, 138, 91, 55, 30, 14, 5, 1, 0, 220, 323, 270, 201, 139, 91 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Row 1:  A002292 Row 2:  A211637 Row 3:  A211651 Limiting row sequence: A000330 Let R be the array in A211796 and let R' be the array in A211799.  Then R(k,n)+R'(k,n)=3^(n-1). See the Comments at A211790. LINKS EXAMPLE Northwest corner: 0...0...1...4....10...20...35...56 0...1...5...13...26...48...78...119 0...1...5...14...29...53...88...134 0...1...5...14...30...55...90...138 0...1...5...14...30...55...91...139 MATHEMATICA z = 48; t[k_, n_] := Module[{s = 0},    (Do[If[w^k > x^k + y^k, s = s + 1],        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]; Table[t[1, n], {n, 1, z}]  (* A000292 *) Table[t[2, n], {n, 1, z}]  (* A211637 *) Table[t[3, n], {n, 1, z}]  (* A211651 *) TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]] Flatten[Table[t[k, n - k + 1],     {n, 1, 12}, {k, 1, n}]] (* A211799 *) Table[k (k - 1) (2 k - 1)/6,     {k, 1, z}] (* row-limit sequence, A000330 *) (* Peter J. C. Moses, Apr 13 2012 *) CROSSREFS Cf. A211790. Sequence in context: A232397 A122753 A016714 * A113950 A269944 A121906 Adjacent sequences:  A211796 A211797 A211798 * A211800 A211801 A211802 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Apr 21 2012 STATUS approved

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Last modified December 10 04:15 EST 2019. Contains 329885 sequences. (Running on oeis4.)