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%I #17 Nov 23 2016 18:37:15
%S 0,1,7,22,50,96,163,255,378,534,730,969,1255,1592,1982,2434,2949,3533,
%T 4188,4918,5732,6629,7617,8696,9876,11154,12539,14037,15646,17378,
%U 19230,21209,23321,25568,27957,30487,33166,36000,38989,42140
%N Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^3 < x^3 + y^3.
%C For a guide to related sequences, see A211422.
%C 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]
%D L. Euler, Vollständige Anleitung zur Algebra, (1770), Roy. Acad. Sci., St. Petersburg.
%H Michael A. Bennett, Vinayak Vatsal and Soroosh Yazdani, <a href="https://doi.org/10.1112/S0010437X04000983">Ternary Diophantine equations of signature (p, p, 3)</a>, Compos. Math. 140 (6) (2004) p. 1399 Theorem 8.1.
%t t = Compile[{{n, _Integer}}, Module[{s = 0},
%t (Do[If[w^3 < x^3 + y^3, s = s + 1],
%t {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]];
%t Map[t[#] &, Range[0, 50]] (* A211650 *)
%t (* _Peter J. C. Moses_, Apr 13 2012 *)
%Y Cf. A211422.
%K nonn
%O 0,3
%A _Clark Kimberling_, Apr 18 2012
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