A211802 R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and 2*w^k < x^k + y^k; square array read by descending antidiagonals.

0, 3, 0, 11, 3, 0, 28, 13, 3, 0, 56, 32, 13, 3, 0, 99, 64, 34, 13, 3, 0, 159, 113, 68, 34, 13, 3, 0, 240, 181, 117, 70, 34, 13, 3, 0, 344, 272, 187, 125, 70, 34, 13, 3, 0, 475, 388, 282, 197, 125, 70, 34, 13, 3, 0, 635, 535, 406, 292, 203, 125, 70, 34, 13, 3, 0

Offset: 1

Author

Clark Kimberling, Apr 22 2012

Keywords

• nonn
• tabl

Comments

Row 1: A182260.

Row 2: A211800.

Row 3: A211801.

Limiting row sequence: A016061.

Let R be the array in this sequence and let R' be the array in A211805. Then R(k,n) + R'(k,n) = 3^(n-1).

See the Comments at A211790.

Examples

			Northwest corner:
  0   3  11  28  56  99 159 240
  0   3  13  32  64 113 181 272
  0   3  13  34  68 117 187 282
  0   3  13  34  70 125 197 292
  0   3  13  34  70 125 203 302
		

Crossrefs

Cf. A016061, A182260, A211790, A211800, A211801, A211802, A211805.

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}]  (* A211800 *)
Table[t[3, n], {n, 1, z}]  (* A211801 *)
TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
Flatten[Table[t[k, n - k + 1], {n, 1, 12},
                {k, 1, n}]] (* this sequence *)
Table[k (k - 1) (4 k + 1)/6, {k, 1,
  z}] (* row-limit sequence, A016061 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Extensions

Definition corrected by Georg Fischer, Sep 10 2022