A211650 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^3 < x^3 + y^3.

0, 1, 7, 22, 50, 96, 163, 255, 378, 534, 730, 969, 1255, 1592, 1982, 2434, 2949, 3533, 4188, 4918, 5732, 6629, 7617, 8696, 9876, 11154, 12539, 14037, 15646, 17378, 19230, 21209, 23321, 25568, 27957, 30487, 33166, 36000, 38989, 42140

Offset: 0

Author

Clark Kimberling, Apr 18 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A211422.

Also the number of ordered triples (w,x,y) with all terms in {1,...,n} and w^3 <= x^3 + y^3. [Note that there are no integer solutions to w^3 = x^3 + y^3, see for example Compos. Math. 140 (6) (2004) p 1399 Theorem 8.1. - R. J. Mathar, Jun 27 2012]

References

• L. Euler, Vollständige Anleitung zur Algebra, (1770), Roy. Acad. Sci., St. Petersburg.

Links

• Michael A. Bennett, Vinayak Vatsal and Soroosh Yazdani, Ternary Diophantine equations of signature (p, p, 3), Compos. Math. 140 (6) (2004) p. 1399 Theorem 8.1.

Crossrefs

Cf. A211422.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
    (Do[If[w^3 < x^3 + y^3, s = s + 1],
        {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A211650 *)
(* Peter J. C. Moses, Apr 13 2012 *)