A211637 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2>x^2+y^2.

0, 0, 1, 5, 13, 26, 48, 78, 119, 173, 240, 323, 421, 538, 677, 837, 1020, 1226, 1460, 1723, 2015, 2337, 2694, 3084, 3508, 3969, 4471, 5016, 5601, 6227, 6900, 7619, 8389, 9208, 10078, 11004, 11981, 13015, 14105, 15258, 16472, 17744, 19083, 20487, 21962, 23505

Offset: 0

Author

Clark Kimberling, Apr 18 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A211422.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A211422.

Programs

Maple

b:= proc(n) option remember; 1+floor(sqrt(n)) end:
a:= proc(n) local c, x, y, w;
      c:= 0;
      for x to n do
        for y from x to n do
          w:= b(x^2+y^2);
          if w>n then break fi;
          c:= c+ (n-w+1)*`if`(x=y, 1, 2)
        od
      od: c
    end:
seq (a(n), n=0..50);  # Alois P. Heinz, May 10 2012

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
    (Do[If[w^2 > x^2 + y^2, s = s + 1],
        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]]   (* A211637 *)
(* Peter J. C. Moses, Apr 13 2012 *)