A211805 Rectangular array: R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^k>=x^k+y

1, 5, 1, 16, 5, 1, 36, 14, 5, 1, 69, 32, 14, 5, 1, 117, 61, 30, 14, 5, 1, 184, 103, 57, 30, 14, 5, 1, 272, 162, 99, 55, 30, 14, 5, 1, 385, 240, 156, 91, 55, 30, 14, 5, 1, 525, 341, 230, 146, 91, 55, 30, 14, 5, 1, 696, 465, 323, 220, 140, 91, 55, 30, 14, 5, 1, 900

Offset: 1

Author

Clark Kimberling, Apr 22 2012

Keywords

• nonn
• tabl

Comments

Row 1: A055232

Row 2: A211803

Row 3: A211804

Limiting row sequence: A000330

Let R be the array in A211802 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:
1...5...16...36...69...117...184
1...5...14...32...61...103...162
1...5...14...30...57...99....156
1...5...14...30...55...91....146
1...5...14...30...55...91....140
		

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}]  (* A055232 *)
Table[t[2, n], {n, 1, z}]  (* A211803 *)
Table[t[3, n], {n, 1, z}]  (* A211804 *)
TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
Flatten[Table[t[k, n - k + 1], {n, 1, 12},
               {k, 1, n}]] (* A211805 *)
Table[k (k + 1) (2 k + 1)/6,
    {k, 1, z}] (* row-limit sequence, A000330 *)
(* Peter J. C. Moses, Apr 13 2012 *)