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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

%I A211799 #5 Dec 04 2016 19:46:28
%S A211799 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,
%T A211799 78,53,30,14,5,1,0,84,119,88,55,30,14,5,1,0,120,173,134,90,55,30,14,5,
%U A211799 1,0,165,240,195,138,91,55,30,14,5,1,0,220,323,270,201,139,91
%N 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<k.
%C A211799 Row 1:  A002292
%C A211799 Row 2:  A211637
%C A211799 Row 3:  A211651
%C A211799 Limiting row sequence: A000330
%C A211799 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).
%C A211799 See the Comments at A211790.
%e A211799 Northwest corner:
%e A211799 0...0...1...4....10...20...35...56
%e A211799 0...1...5...13...26...48...78...119
%e A211799 0...1...5...14...29...53...88...134
%e A211799 0...1...5...14...30...55...90...138
%e A211799 0...1...5...14...30...55...91...139
%t A211799 z = 48;
%t A211799 t[k_, n_] := Module[{s = 0},
%t A211799    (Do[If[w^k > x^k + y^k, s = s + 1],
%t A211799        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)];
%t A211799 Table[t[1, n], {n, 1, z}]  (* A000292 *)
%t A211799 Table[t[2, n], {n, 1, z}]  (* A211637 *)
%t A211799 Table[t[3, n], {n, 1, z}]  (* A211651 *)
%t A211799 TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
%t A211799 Flatten[Table[t[k, n - k + 1],
%t A211799     {n, 1, 12}, {k, 1, n}]] (* A211799 *)
%t A211799 Table[k (k - 1) (2 k - 1)/6,
%t A211799     {k, 1, z}] (* row-limit sequence, A000330 *)
%t A211799 (* _Peter J. C. Moses_, Apr 13 2012 *)
%Y A211799 Cf. A211790.
%K A211799 nonn,tabl
%O A211799 1,7
%A A211799 _Clark Kimberling_, Apr 21 2012