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