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A211650
Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^3 < x^3 + y^3.
4
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
0,3
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.
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 *)
CROSSREFS
Cf. A211422.
Sequence in context: A224141 A002412 A211652 * A211792 A211635 A211634
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 18 2012
STATUS
approved