A212098 Number of (w,x,y,z) with all terms in {1,...,n} and w^3<=x^3+y^3+z^3.

0, 1, 15, 72, 221, 536, 1104, 2034, 3451, 5514, 8380, 12246, 17322, 23812, 31981, 42107, 54457, 69350, 87100, 108049, 132591, 161085, 193966, 231592, 274511, 323077, 377830, 439314, 507948, 584401, 669124, 762764, 865882, 979130

Offset: 0

Author

Clark Kimberling, May 03 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A211795.

Links

• Giovanni Resta, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A211795, A212099.

Programs

Maple

f:= proc(n) local x,y,z, r, t;
   r:= 0:
   for x from 1 to n do
     for y from x to n do
       for z from y to n do
          t:= min(n, floor((x^3 + y^3 + z^3)^(1/3)));
          if x = z then r:= r+t
          elif x=y or y=z then r:= r+3*t
          else r:= r+6*t
          fi
   od od od;
   r
end proc:
map(f, [$0..40]); # Robert Israel, May 08 2017

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w^3 <= x^3 + y^3 + z^3, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212098 *)
(* Peter J. C. Moses, Apr 13 2012 *)

PARI

A212098(n)={my(s=0,c=[6,3,1]);forvec(v=vector(4,i,if(i>1,[1,n],[-n,-1])),sum(i=1,4,v[i]^3)>=0&s+=c[1+(v[2]==v[3])+(v[3]==v[4])],1);s} /* not very efficient */ \\ M. F. Hasler, May 20 2012

Formula

a(n) + A212099(n) = n^4.