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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row 1:  A000292

Row 2:  A211636

Row 3:  A211651

Limiting row sequence: A000330

Let R be the array in A211790 and let R' be the array in A211793.  Then R(k,n)+R'(k,n)=3^(n-1).

See the Comments at A211790.

LINKS

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

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}]] (* A211793 *)

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.

Sequence in context: A284982 A089962 A127155 * A145880 A048516 A060638

Adjacent sequences:  A211790 A211791 A211792 * A211794 A211795 A211796

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Apr 21 2012

STATUS

approved

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Last modified April 15 18:51 EDT 2021. Contains 342977 sequences. (Running on oeis4.)