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A211808 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 A211808 #5 Dec 04 2016 19:46:28
%S A211808 1,5,1,16,5,1,36,16,5,1,69,36,16,5,1,117,69,38,16,5,1,184,119,73,38,
%T A211808 16,5,1,272,190,123,75,38,16,5,1,385,282,194,131,75,38,16,5,1,525,399,
%U A211808 290,204,131,75,38,16,5,1,696,547,415,300,210,131,75,38,16,5,1
%N A211808 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 A211808 Row 1:  A055232
%C A211808 Row 2:  A211806
%C A211808 Row 3:  A211807
%C A211808 Limiting row sequence: A000330
%C A211808 Let R be the array in A211808 and let R' be the array in A182259.  Then R(k,n)+R'(k,n)=3^(n-1).
%C A211808 See the Comments at A211790.
%e A211808 Northwest corner:
%e A211808 1...5...16...36...69...117...184
%e A211808 1...5...16...36...69...119...190
%e A211808 1...5...16...38...73...123...194
%e A211808 1...5...16...38...75...131...204
%e A211808 1...5...16...38...75...131...210
%t A211808 z = 48;
%t A211808 t[k_, n_] := Module[{s = 0},
%t A211808    (Do[If[2 w^k <= x^k + y^k, s = s + 1],
%t A211808        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)];
%t A211808 Table[t[1, n], {n, 1, z}]  (* A055232 *)
%t A211808 Table[t[2, n], {n, 1, z}]  (* A211806 *)
%t A211808 Table[t[3, n], {n, 1, z}]  (* A211807 *)
%t A211808 TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
%t A211808 Flatten[Table[t[k, n - k + 1],
%t A211808      {n, 1, 12}, {k, 1, n}]] (* A211808 *)
%t A211808 Table[k (4 k^2 - 3 k + 5)/6,
%t A211808      {k, 1, z}] (* row-limit sequence, A174723 *)
%t A211808 (* _Peter J. C. Moses_, Apr 13 2012 *)
%Y A211808 Cf. A211790.
%K A211808 nonn,tabl
%O A211808 1,2
%A A211808 _Clark Kimberling_, Apr 22 2012