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A211796 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
1, 8, 1, 26, 7, 1, 60, 22, 7, 1, 115, 51, 22, 7, 1, 196, 99, 50, 22, 7, 1, 308, 168, 96, 50, 22, 7, 1, 456, 265, 163, 95, 50, 22, 7, 1, 645, 393, 255, 161, 95, 50, 22, 7, 1, 880, 556, 378, 253, 161, 95, 50, 22, 7, 1, 1166, 760, 534, 374, 252, 161, 95, 50, 22, 7 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 1:  A002413

Row 2:  A211634

Row 3:  A211650

Limiting row sequence: A002412

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..65.

EXAMPLE

Northwest corner:

1...8...26...60...115...196...308

1...7...22...51...99....168...265

1...7...22...50...96....163...255

1...7...22...50...95....161...253

1...7...22...50...95....161...252

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}]  (* A002413 *)

Table[t[2, n], {n, 1, z}]  (* A211634 *)

Table[t[3, n], {n, 1, z}]  (* A211650 *)

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

Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* A211796 *)

Table[k (k - 1) (2 k - 1)/6, {k, 1,

  z}] (* row-limit sequence, A002412 *)

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

CROSSREFS

Cf. A211790.

Sequence in context: A125235 A183892 A019432 * A138505 A002173 A050458

Adjacent sequences:  A211793 A211794 A211795 * A211797 A211798 A211799

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.)