A211793 Rectangular array: R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and w^k >= x^k + y^k.

0, 1, 0, 4, 1, 0, 10, 5, 1, 0, 20, 13, 5, 1, 0, 35, 28, 14, 5, 1, 0, 56, 50, 29, 14, 5, 1, 0, 84, 80, 53, 30, 14, 5, 1, 0, 120, 121, 88, 55, 30, 14, 5, 1, 0, 165, 175, 134, 90, 55, 30, 14, 5, 1, 0, 220, 244, 195, 138, 91, 55, 30, 14, 5, 1, 0, 286, 327, 270, 201, 139

Offset: 1

Author

Clark Kimberling, Apr 21 2012

Keywords

• nonn
• tabl

Comments

Limiting row sequence: A000330.

Examples

			Northwest corner:
  0, 1, 4, 10, 20, 35, 56,  84
  0, 1, 5, 13, 28, 50, 80, 121
  0, 1, 5, 14, 29, 53, 88, 134
  0, 1, 5, 14, 30, 55, 90, 138
  0, 1, 5, 14, 30, 55, 91, 139
  0, 1, 5, 14, 30, 55, 91, 140
		

Crossrefs

Cf. A211790.

Cf. A000292 (row 1), A211636 (row 2), A211651 (row 3), A000330.

Programs

Mathematica

z = 48;
t[k_, n_] := Module[{s = 0},
   (Do[If[w^k >= x^k + y^k, s = s + 1],
       {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)];
Table[t[1, n], {n, 1, z}]  (* A000292 *)
Table[t[2, n], {n, 1, z}]  (* A211636 *)
Table[t[3, n], {n, 1, z}]  (* A211651 *)
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) (2 k - 1)/6, {k, 1,
  z}] (* row-limit sequence, A000330 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Formula

A211790(k,n) + R(k,n) = 3^(n-1).