A211802 R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and 2*w^k < x^k + y^k; square array read by descending antidiagonals.

0, 3, 0, 11, 3, 0, 28, 13, 3, 0, 56, 32, 13, 3, 0, 99, 64, 34, 13, 3, 0, 159, 113, 68, 34, 13, 3, 0, 240, 181, 117, 70, 34, 13, 3, 0, 344, 272, 187, 125, 70, 34, 13, 3, 0, 475, 388, 282, 197, 125, 70, 34, 13, 3, 0, 635, 535, 406, 292, 203, 125, 70, 34, 13, 3, 0

Offset

1,2

Comments

Row 1: A182260.

Row 2: A211800.

Row 3: A211801.

Limiting row sequence: A016061.

Let R be the array in this sequence and let R' be the array in A211805. Then R(k,n) + R'(k,n) = 3^(n-1).

See the Comments at A211790.

Links

Table of n, a(n) for n=1..66.

Example

Northwest corner:
  0   3  11  28  56  99 159 240
  0   3  13  32  64 113 181 272
  0   3  13  34  68 117 187 282
  0   3  13  34  70 125 197 292
  0   3  13  34  70 125 203 302

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}]  (* A182260 *)
Table[t[2, n], {n, 1, z}]  (* A211800 *)
Table[t[3, n], {n, 1, z}]  (* A211801 *)
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) (4 k + 1)/6, {k, 1,
  z}] (* row-limit sequence, A016061 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Crossrefs

Cf. A016061, A182260, A211790, A211800, A211801, A211802, A211805.

Sequence in context: A346240 A216470 A182259 * A249775 A019264 A028851

Adjacent sequences: A211799 A211800 A211801 * A211803 A211804 A211805

Keyword

nonn,tabl

Author

Clark Kimberling, Apr 22 2012

Extensions

Definition corrected by Georg Fischer, Sep 10 2022

Status

approved