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A211793 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.

%I A211793 #28 Oct 28 2023 15:27:42
%S A211793 0,1,0,4,1,0,10,5,1,0,20,13,5,1,0,35,28,14,5,1,0,56,50,29,14,5,1,0,84,
%T A211793 80,53,30,14,5,1,0,120,121,88,55,30,14,5,1,0,165,175,134,90,55,30,14,
%U A211793 5,1,0,220,244,195,138,91,55,30,14,5,1,0,286,327,270,201,139
%N A211793 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 A211793 Limiting row sequence: A000330.
%F A211793 A211790(k,n) + R(k,n) = 3^(n-1).
%e A211793 Northwest corner:
%e A211793   0, 1, 4, 10, 20, 35, 56,  84
%e A211793   0, 1, 5, 13, 28, 50, 80, 121
%e A211793   0, 1, 5, 14, 29, 53, 88, 134
%e A211793   0, 1, 5, 14, 30, 55, 90, 138
%e A211793   0, 1, 5, 14, 30, 55, 91, 139
%e A211793   0, 1, 5, 14, 30, 55, 91, 140
%t A211793 z = 48;
%t A211793 t[k_, n_] := Module[{s = 0},
%t A211793    (Do[If[w^k >= x^k + y^k, s = s + 1],
%t A211793        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)];
%t A211793 Table[t[1, n], {n, 1, z}]  (* A000292 *)
%t A211793 Table[t[2, n], {n, 1, z}]  (* A211636 *)
%t A211793 Table[t[3, n], {n, 1, z}]  (* A211651 *)
%t A211793 TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
%t A211793 Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* this sequence *)
%t A211793 Table[k (k - 1) (2 k - 1)/6, {k, 1,
%t A211793   z}] (* row-limit sequence, A000330 *)
%t A211793 (* _Peter J. C. Moses_, Apr 13 2012 *)
%Y A211793 Cf. A211790.
%Y A211793 Cf. A000292 (row 1), A211636 (row 2), A211651 (row 3), A000330.
%K A211793 nonn,tabl
%O A211793 1,4
%A A211793 _Clark Kimberling_, Apr 21 2012