A211793 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.

0, 1, 0, 4, 1, 0, 10, 5, 1, 0, 20, 13, 5, 1, 0, 35, 28, 14, 5, 1, 0, 56, 50, 29, 14, 5, 1, 0, 84, 80, 53, 30, 14, 5, 1, 0, 120, 121, 88, 55, 30, 14, 5, 1, 0, 165, 175, 134, 90, 55, 30, 14, 5, 1, 0, 220, 244, 195, 138, 91, 55, 30, 14, 5, 1, 0, 286, 327, 270, 201, 139

Offset

1,4

Comments

Limiting row sequence: A000330.

Links

Table of n, a(n) for n=1..71.

Formula

A211790(k,n) + R(k,n) = 3^(n-1).

Example

Northwest corner:
  0, 1, 4, 10, 20, 35, 56,  84
  0, 1, 5, 13, 28, 50, 80, 121
  0, 1, 5, 14, 29, 53, 88, 134
  0, 1, 5, 14, 30, 55, 90, 138
  0, 1, 5, 14, 30, 55, 91, 139
  0, 1, 5, 14, 30, 55, 91, 140

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}]  (* A211636 *)
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}]] (* this sequence *)
Table[k (k - 1) (2 k - 1)/6, {k, 1,
  z}] (* row-limit sequence, A000330 *)
(* Peter J. C. Moses, Apr 13 2012 *)

Crossrefs

Cf. A211790.

Cf. A000292 (row 1), A211636 (row 2), A211651 (row 3), A000330.

Sequence in context: A089962 A363971 A127155 * A145880 A048516 A060638

Adjacent sequences: A211790 A211791 A211792 * A211794 A211795 A211796

Keyword

nonn,tabl

Author

Clark Kimberling, Apr 21 2012

Status

approved