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A211791 Number of ordered triples (w,x,y) such that x and y are in {1,...,n} and w^2<=x^2+y^2. 3
1, 7, 23, 54, 103, 175, 276, 409, 579, 791, 1050, 1360, 1724, 2149, 2640, 3198, 3832, 4543, 5337, 6217, 7192, 8265, 9437, 10716, 12103, 13609, 15231, 16978, 18857, 20869, 23018, 25307, 27745, 30337, 33084, 35992, 39066, 42309, 45728 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 2 of A211798.

LINKS

Table of n, a(n) for n=1..39.

FORMULA

Sum{sum{floor((x^2+y^2)^(1/2)), 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: A038796 A332492 A304724 * A004068 A261893 A022815

Adjacent sequences:  A211788 A211789 A211790 * A211792 A211793 A211794

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 26 2012

STATUS

approved

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Last modified April 15 20:35 EDT 2021. Contains 342977 sequences. (Running on oeis4.)