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A211805 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. 5
1, 5, 1, 16, 5, 1, 36, 14, 5, 1, 69, 32, 14, 5, 1, 117, 61, 30, 14, 5, 1, 184, 103, 57, 30, 14, 5, 1, 272, 162, 99, 55, 30, 14, 5, 1, 385, 240, 156, 91, 55, 30, 14, 5, 1, 525, 341, 230, 146, 91, 55, 30, 14, 5, 1, 696, 465, 323, 220, 140, 91, 55, 30, 14, 5, 1, 900 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 1:  A055232

Row 2:  A211803

Row 3:  A211804

Limiting row sequence: A000330

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..67.

EXAMPLE

Northwest corner:

1...5...16...36...69...117...184

1...5...14...32...61...103...162

1...5...14...30...57...99....156

1...5...14...30...55...91....146

1...5...14...30...55...91....140

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}]  (* A055232 *)

Table[t[2, n], {n, 1, z}]  (* A211803 *)

Table[t[3, n], {n, 1, z}]  (* A211804 *)

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

Flatten[Table[t[k, n - k + 1], {n, 1, 12},

               {k, 1, n}]] (* A211805 *)

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: A283434 A019429 A221364 * A211808 A093826 A144699

Adjacent sequences:  A211802 A211803 A211804 * A211806 A211807 A211808

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Apr 22 2012

STATUS

approved

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Last modified March 28 19:41 EDT 2020. Contains 333103 sequences. (Running on oeis4.)