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A182259 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, 11, 3, 0, 56, 28, 11, 3, 0, 99, 56, 26, 11, 3, 0, 159, 97, 52, 26, 11, 3, 0, 240, 153, 93, 50, 26, 11, 3, 0, 344, 230, 149, 85, 50, 26, 11, 3, 0, 475, 330, 222, 139, 85, 50, 26, 11, 3, 0, 635, 453, 314, 212, 133, 85, 50, 26, 11, 3, 0, 828 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 1:  A182260

Row 2:  A211810

Row 3:  A211811

Limiting row sequence: A051925

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.

LINKS

Table of n, a(n) for n=1..67.

EXAMPLE

Northwest corner (with antidiagonals read from northeast to southwest):

0...3...11...28...56...99...159

0...3...11...28...56...97...153

0...3...11...26...52...93...149

0...3...11...26...50...85...139

0...3...11...26...50...85...133

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}]  (* A211810 *)

Table[t[3, n], {n, 1, z}]  (* A211811 *)

TableForm[Table[t[k, n], {k, 1, 12}, {n, 1, 16}]]

Flatten[Table[t[k, n - k + 1],

    {n, 1, 12}, {k, 1, n}]] (* A182259 *)

Table[k (k - 1) (2 k + 5)/6,

    {k, 1, z}] (* row-limit sequence, A051925 *)

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

CROSSREFS

Cf. A211790.

Sequence in context: A252096 A346240 A216470 * A211802 A249775 A019264

Adjacent sequences:  A182256 A182257 A182258 * A182260 A182261 A182262

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Apr 22 2012

STATUS

approved

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Last modified October 24 20:35 EDT 2021. Contains 348233 sequences. (Running on oeis4.)