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 A211796 Rectangular array:  R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and w^k<=x^k+y^k. 3
 1, 8, 1, 26, 7, 1, 60, 22, 7, 1, 115, 51, 22, 7, 1, 196, 99, 50, 22, 7, 1, 308, 168, 96, 50, 22, 7, 1, 456, 265, 163, 95, 50, 22, 7, 1, 645, 393, 255, 161, 95, 50, 22, 7, 1, 880, 556, 378, 253, 161, 95, 50, 22, 7, 1, 1166, 760, 534, 374, 252, 161, 95, 50, 22, 7 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row 1:  A002413 Row 2:  A211634 Row 3:  A211650 Limiting row sequence: A002412 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: 1...8...26...60...115...196...308 1...7...22...51...99....168...265 1...7...22...50...96....163...255 1...7...22...50...95....161...253 1...7...22...50...95....161...252 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}]  (* A002413 *) Table[t[2, n], {n, 1, z}]  (* A211634 *) Table[t[3, n], {n, 1, z}]  (* A211650 *) TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]] Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* A211796 *) Table[k (k - 1) (2 k - 1)/6, {k, 1,   z}] (* row-limit sequence, A002412 *) (* Peter J. C. Moses, Apr 13 2012 *) CROSSREFS Cf. A211790. Sequence in context: A125235 A183892 A019432 * A138505 A002173 A050458 Adjacent sequences:  A211793 A211794 A211795 * A211797 A211798 A211799 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Apr 21 2012 STATUS approved

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Last modified April 15 20:40 EDT 2021. Contains 342977 sequences. (Running on oeis4.)