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%I #17 Jan 13 2019 12:05:12
%S 2,31,80,120,282,17,525,437,386,2479,5253,3268,2952,3875,8894,7182,
%T 9457,16397,3401,8629,1830,2518,19976,37326,55340,21182,98642,56358,
%U 150673,17220,211196,185129,223680,98763,219284,138712,145330,532762,676971,68490,776927,405452,26488
%N Consider all integer triples (i,j,k), j >= k > 0, with binomial(i+2,3)=j^3+k^3, ordered by increasing i; sequence gives k values.
%C The i values are in A054205 and j values in A054206.
%H Bert Dobbelaere, <a href="/A054207/b054207.txt">Table of n, a(n) for n = 1..53</a>
%e binomial(5+2,3)=35=2^3+3^3; binomial(95+2,3)=147440=49^3+31^3;
%t lst = {}; Do[ b = Binomial[i + 2, 3]; j = Floor[b^(1/3)]; lmt = Ceiling[j/2]; While[ k = (b - j^3)^(1/3); j > lmt && !IntegerQ[k], j-- ]; If[j != lmt, Print[{i, j, k}]; AppendTo[lst, {i, j, k}]], {i, 2, 30000}]; Last /@ lst (* _Robert G. Wilson v_, Jan 15 2007 *)
%Y Cf. A054205, A054206, A000292.
%K nice,nonn
%O 1,1
%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 28 2000
%E More terms from _Martin Fuller_, Nov 27 2006
%E Offset corrected by _N. J. A. Sloane_, Jan 14 2009
%E a(30)-a(36) from _Jon E. Schoenfield_, Jan 14 2009
%E a(37)-a(43) from _Jon E. Schoenfield_, Aug 30 2013
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