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A182259 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 A182259 #6 Dec 04 2016 19:46:24
%S A182259 0,3,0,11,3,0,28,11,3,0,56,28,11,3,0,99,56,26,11,3,0,159,97,52,26,11,
%T A182259 3,0,240,153,93,50,26,11,3,0,344,230,149,85,50,26,11,3,0,475,330,222,
%U A182259 139,85,50,26,11,3,0,635,453,314,212,133,85,50,26,11,3,0,828
%N A182259 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 A182259 Row 1:  A182260
%C A182259 Row 2:  A211810
%C A182259 Row 3:  A211811
%C A182259 Limiting row sequence: A051925
%C A182259 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 A182259 See the Comments at A211790.
%e A182259 Northwest corner (with antidiagonals read from northeast to southwest):
%e A182259 0...3...11...28...56...99...159
%e A182259 0...3...11...28...56...97...153
%e A182259 0...3...11...26...52...93...149
%e A182259 0...3...11...26...50...85...139
%e A182259 0...3...11...26...50...85...133
%t A182259 z = 48;
%t A182259 t[k_, n_] := Module[{s = 0},
%t A182259    (Do[If[2 w^k > x^k + y^k, s = s + 1],
%t A182259        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)];
%t A182259 Table[t[1, n], {n, 1, z}]  (* A182260 *)
%t A182259 Table[t[2, n], {n, 1, z}]  (* A211810 *)
%t A182259 Table[t[3, n], {n, 1, z}]  (* A211811 *)
%t A182259 TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
%t A182259 Flatten[Table[t[k, n - k + 1],
%t A182259     {n, 1, 12}, {k, 1, n}]] (* A182259 *)
%t A182259 Table[k (k - 1) (2 k + 5)/6,
%t A182259     {k, 1, z}] (* row-limit sequence, A051925 *)
%t A182259 (* _Peter J. C. Moses_, Apr 13 2012 *)
%Y A182259 Cf. A211790.
%K A182259 nonn,tabl
%O A182259 1,2
%A A182259 _Clark Kimberling_, Apr 22 2012