A216877 Number of ordered integers (x,y) satisfying x^(2/3) + y^(2/3) <= n^(2/3).

1, 5, 9, 17, 21, 33, 49, 61, 81, 105, 125, 145, 169, 205, 233, 273, 309, 357, 393, 437, 485, 529, 565, 629, 681, 741, 805, 873, 933, 997, 1073, 1133, 1205, 1289, 1377, 1453, 1537, 1633, 1725, 1793, 1889, 1989, 2081, 2177, 2293, 2393, 2497, 2621, 2721, 2833

Offset

0,2

Comments

Lattice points in x^(2/3) + y^(2/3) <= n^(2/3).

Links

Table of n, a(n) for n=0..49.

Maple

count := proc(n)
    local t, x, y;
    t := 0;
    for x from 1 to n-1 do
      for y from 1 to n-x do
        if evalf(x^(2/3)+y^(2/3)-n^(2/3)) <= 0 then
          t := t+1
        end if:
      end do:
    end do;
    return 4*t+4*n+1:
  end proc;
  S := [seq(count(a), a = 0 .. 41)];

Mathematica

Table[cnt = 0; Do[If[x^(2/3) + y^(2/3) <= n^(2/3), cnt++], {x, n}, {y, n}]; 4*cnt + 4*n + 1, {n, 0, 50}] (* T. D. Noe, Sep 18 2012 *)

Crossrefs

Sequence in context: A288448 A022341 A255651 * A350989 A268756 A095725

Adjacent sequences: A216874 A216875 A216876 * A216878 A216879 A216880

Keyword

nonn

Author

César Eliud Lozada, Sep 18 2012

Status

approved