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

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, 3, 0, 240, 153, 93, 50, 26, 11, 3, 0, 344, 230, 149, 85, 50, 26, 11, 3, 0, 475, 330, 222, 139, 85, 50, 26, 11, 3, 0, 635, 453, 314, 212, 133, 85, 50, 26, 11, 3, 0, 828

Offset: 1

Author

Clark Kimberling, Apr 22 2012

Keywords

• nonn
• tabl

Comments

Row 1: A182260

Row 2: A211810

Row 3: A211811

Limiting row sequence: A051925

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).

See the Comments at A211790.

Examples

			Northwest corner (with antidiagonals read from northeast to southwest):
0...3...11...28...56...99...159
0...3...11...28...56...97...153
0...3...11...26...52...93...149
0...3...11...26...50...85...139
0...3...11...26...50...85...133
		

Crossrefs

Cf. A211790.

Programs

Mathematica

z = 48;
t[k_, n_] := Module[{s = 0},
   (Do[If[2 w^k > x^k + y^k, s = s + 1],
       {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)];
Table[t[1, n], {n, 1, z}]  (* A182260 *)
Table[t[2, n], {n, 1, z}]  (* A211810 *)
Table[t[3, n], {n, 1, z}]  (* A211811 *)
TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
Flatten[Table[t[k, n - k + 1],
    {n, 1, 12}, {k, 1, n}]] (* A182259 *)
Table[k (k - 1) (2 k + 5)/6,
    {k, 1, z}] (* row-limit sequence, A051925 *)
(* Peter J. C. Moses, Apr 13 2012 *)