A211796 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.

1, 8, 1, 26, 7, 1, 60, 22, 7, 1, 115, 51, 22, 7, 1, 196, 99, 50, 22, 7, 1, 308, 168, 96, 50, 22, 7, 1, 456, 265, 163, 95, 50, 22, 7, 1, 645, 393, 255, 161, 95, 50, 22, 7, 1, 880, 556, 378, 253, 161, 95, 50, 22, 7, 1, 1166, 760, 534, 374, 252, 161, 95, 50, 22, 7

Offset: 1

Author

Clark Kimberling, Apr 21 2012

Keywords

• nonn
• tabl

Comments

Row 1: A002413

Row 2: A211634

Row 3: A211650

Limiting row sequence: A002412

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:
1...8...26...60...115...196...308
1...7...22...51...99....168...265
1...7...22...50...96....163...255
1...7...22...50...95....161...253
1...7...22...50...95....161...252
		

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}]  (* A002413 *)
Table[t[2, n], {n, 1, z}]  (* A211634 *)
Table[t[3, n], {n, 1, z}]  (* A211650 *)
TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* A211796 *)
Table[k (k - 1) (2 k - 1)/6, {k, 1,
  z}] (* row-limit sequence, A002412 *)
(* Peter J. C. Moses, Apr 13 2012 *)