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A211799 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. 3
0, 0, 0, 1, 1, 0, 4, 5, 1, 0, 10, 13, 5, 1, 0, 20, 26, 14, 5, 1, 0, 35, 48, 29, 14, 5, 1, 0, 56, 78, 53, 30, 14, 5, 1, 0, 84, 119, 88, 55, 30, 14, 5, 1, 0, 120, 173, 134, 90, 55, 30, 14, 5, 1, 0, 165, 240, 195, 138, 91, 55, 30, 14, 5, 1, 0, 220, 323, 270, 201, 139, 91 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Row 1:  A002292

Row 2:  A211637

Row 3:  A211651

Limiting row sequence: A000330

Let R be the array in A211796 and let R' be the array in A211799.  Then R(k,n)+R'(k,n)=3^(n-1).

See the Comments at A211790.

LINKS

Table of n, a(n) for n=1..72.

EXAMPLE

Northwest corner:

0...0...1...4....10...20...35...56

0...1...5...13...26...48...78...119

0...1...5...14...29...53...88...134

0...1...5...14...30...55...90...138

0...1...5...14...30...55...91...139

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}]  (* A211637 *)

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}]] (* A211799 *)

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: A232397 A122753 A016714 * A113950 A269944 A121906

Adjacent sequences:  A211796 A211797 A211798 * A211800 A211801 A211802

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Apr 21 2012

STATUS

approved

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Last modified April 15 20:40 EDT 2021. Contains 342977 sequences. (Running on oeis4.)