A211799 Rectangular array: R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and w^k<=x^k+y

0, 0, 0, 1, 1, 0, 4, 5, 1, 0, 10, 13, 5, 1, 0, 20, 26, 14, 5, 1, 0, 35, 48, 29, 14, 5, 1, 0, 56, 78, 53, 30, 14, 5, 1, 0, 84, 119, 88, 55, 30, 14, 5, 1, 0, 120, 173, 134, 90, 55, 30, 14, 5, 1, 0, 165, 240, 195, 138, 91, 55, 30, 14, 5, 1, 0, 220, 323, 270, 201, 139, 91

Offset: 1

Author

Clark Kimberling, Apr 21 2012

Keywords

• nonn
• tabl

Comments

Row 1: A002292

Row 2: A211637

Row 3: A211651

Limiting row sequence: A000330

Let R be the array in A211796 and let R' be the array in A211799. Then R(k,n)+R'(k,n)=3^(n-1).

See the Comments at A211790.

Examples

			Northwest corner:
0...0...1...4....10...20...35...56
0...1...5...13...26...48...78...119
0...1...5...14...29...53...88...134
0...1...5...14...30...55...90...138
0...1...5...14...30...55...91...139
		

Crossrefs

Cf. A211790.

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}]  (* A211637 *)
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}]] (* A211799 *)
Table[k (k - 1) (2 k - 1)/6,
    {k, 1, z}] (* row-limit sequence, A000330 *)
(* Peter J. C. Moses, Apr 13 2012 *)