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A211805 Rectangular array: R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^k>=x^k+y

%I A211805 #5 Dec 04 2016 19:46:28
%S A211805 1,5,1,16,5,1,36,14,5,1,69,32,14,5,1,117,61,30,14,5,1,184,103,57,30,
%T A211805 14,5,1,272,162,99,55,30,14,5,1,385,240,156,91,55,30,14,5,1,525,341,
%U A211805 230,146,91,55,30,14,5,1,696,465,323,220,140,91,55,30,14,5,1,900
%N A211805 Rectangular array:  R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^k>=x^k+y<k.
%C A211805 Row 1:  A055232
%C A211805 Row 2:  A211803
%C A211805 Row 3:  A211804
%C A211805 Limiting row sequence: A000330
%C A211805 Let R be the array in A211802 and let R' be the array in A211805.  Then R(k,n)+R'(k,n)=3^(n-1).
%C A211805 See the Comments at A211790.
%e A211805 Northwest corner:
%e A211805 1...5...16...36...69...117...184
%e A211805 1...5...14...32...61...103...162
%e A211805 1...5...14...30...57...99....156
%e A211805 1...5...14...30...55...91....146
%e A211805 1...5...14...30...55...91....140
%t A211805 z = 48;
%t A211805 t[k_, n_] := Module[{s = 0},
%t A211805    (Do[If[2 w^k >= x^k + y^k, s = s + 1],
%t A211805        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)];
%t A211805 Table[t[1, n], {n, 1, z}]  (* A055232 *)
%t A211805 Table[t[2, n], {n, 1, z}]  (* A211803 *)
%t A211805 Table[t[3, n], {n, 1, z}]  (* A211804 *)
%t A211805 TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
%t A211805 Flatten[Table[t[k, n - k + 1], {n, 1, 12},
%t A211805                {k, 1, n}]] (* A211805 *)
%t A211805 Table[k (k + 1) (2 k + 1)/6,
%t A211805     {k, 1, z}] (* row-limit sequence, A000330 *)
%t A211805 (* _Peter J. C. Moses_, Apr 13 2012 *)
%Y A211805 Cf. A211790.
%K A211805 nonn,tabl
%O A211805 1,2
%A A211805 _Clark Kimberling_, Apr 22 2012