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A211802 Rectangular array:  R(k,n) = number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w^k<x^k+y<k. 6
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 1:  A182260

Row 2:  A211800

Row 3:  A211801

Limiting row sequence: A016061

Let R be the array in A211802 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}]] (* A211802 *)

Table[k (k - 1) (4 k + 1)/6, {k, 1,

  z}] (* row-limit sequence, A016061 *)

(* Peter J. C. Moses, Apr 13 2012 *)

CROSSREFS

Cf. A211790.

Sequence in context: A252096 A216470 A182259 * A249775 A019264 A028851

Adjacent sequences:  A211799 A211800 A211801 * A211803 A211804 A211805

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Apr 22 2012

STATUS

approved

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