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A211792 Number of ordered triples (w,x,y) such that x and y are in {1,...,n} and w^3<=x^3+y^3. 3
1, 7, 22, 51, 97, 164, 258, 382, 541, 741, 982, 1271, 1611, 2008, 2466, 2986, 3577, 4241, 4982, 5807, 6715, 7714, 8808, 10000, 11297, 12701, 14217, 15848, 17600, 19477, 21482, 23620, 25895, 28313, 30879, 33592, 36460, 39487, 42678, 46036 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 3 of A211798.

LINKS

Table of n, a(n) for n=1..40.

FORMULA

Sum{sum{floor((x^3+y^3)^(1/3)), 1<=x<=n, 1<=y<=n}}.

EXAMPLE

The 7 triples counted by a(2): (1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,2), (2,2,1), (2,2,2).

MATHEMATICA

f[x_, y_, k_] := f[x, y, k] = Floor[(x^k + y^k)^(1/k)]

t[k_, n_] := Sum[Sum[f[x, y, k], {x, 1, n}], {y, 1, n}]

Table[t[1, n], {n, 1, 45}]  (* 2*A002411 *)

Table[t[2, n], {n, 1, 45}]  (* A211791 *)

Table[t[3, n], {n, 1, 45}]  (* A211792 *)

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

                 {n, 1, 16}]] (* A211798 *)

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

CROSSREFS

Cf. A211798.

Sequence in context: A002412 A211652 A211650 * A211635 A211634 A184629

Adjacent sequences:  A211789 A211790 A211791 * A211793 A211794 A211795

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 26 2012

STATUS

approved

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Last modified October 27 18:40 EDT 2021. Contains 348287 sequences. (Running on oeis4.)