A182259 - OEIS

%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