A211808 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, 16, 5, 1, 69, 36, 16, 5, 1, 117, 69, 38, 16, 5, 1, 184, 119, 73, 38, 16, 5, 1, 272, 190, 123, 75, 38, 16, 5, 1, 385, 282, 194, 131, 75, 38, 16, 5, 1, 525, 399, 290, 204, 131, 75, 38, 16, 5, 1, 696, 547, 415, 300, 210, 131, 75, 38, 16, 5, 1

Offset: 1

Author

Clark Kimberling, Apr 22 2012

Keywords

• nonn
• tabl

Comments

Row 1: A055232

Row 2: A211806

Row 3: A211807

Limiting row sequence: A000330

Let R be the array in A211808 and let R' be the array in A182259. 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...16...36...69...119...190
1...5...16...38...73...123...194
1...5...16...38...75...131...204
1...5...16...38...75...131...210
		

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}]  (* A211806 *)
Table[t[3, n], {n, 1, z}]  (* A211807 *)
TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]
Flatten[Table[t[k, n - k + 1],
     {n, 1, 12}, {k, 1, n}]] (* A211808 *)
Table[k (4 k^2 - 3 k + 5)/6,
     {k, 1, z}] (* row-limit sequence, A174723 *)
(* Peter J. C. Moses, Apr 13 2012 *)