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 A054209 Consider all integer triples (i,j,k), j >= k>0, with i^3=binomial(j+2,3)+binomial(k+2,3), ordered by increasing i; sequence gives j values. 3
 2, 19, 74, 113, 197, 482, 1162, 1959, 1937, 5644, 6061, 10788, 12772, 17624, 19401, 16503, 29195, 25487, 60881, 63348, 89133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS i values are A054208 and k values are A054210. LINKS EXAMPLE 2^3=8=binomial(2+2,3)+binomial(2+2,3); 11^3=1331=binomial(19+2,3)+binomial(3,3); MATHEMATICA (* This is just a re-computation from A054208 *) A054208 = {2, 11, 45, 65, 109, 280, 644, 1079, 1309, 3180, 3355, 6864, 8284, 9700, 10681, 10856, 16775, 17094, 33506, 35650, 50435}; ijk = Table[ sol = {i, j, k} /. ToRules[ Reduce[ 0 < k <= j && 6*i^3 == j*(j+1)*(j+2) + k*(k+1)*(k+2), {j, k}, Integers]]; Print[sol]; sol, {i, A054208 }]; A054209 = ijk[[All, 2]] (* Jean-François Alcover, Sep 11 2012 *) CROSSREFS Cf. A054208, A054210. Sequence in context: A024389 A110050 A219121 * A256112 A272053 A317274 Adjacent sequences:  A054206 A054207 A054208 * A054210 A054211 A054212 KEYWORD nonn,nice AUTHOR Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 31 2000 EXTENSIONS More terms from Sascha Kurz, Mar 22 2002 STATUS approved

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Last modified May 9 11:55 EDT 2021. Contains 343740 sequences. (Running on oeis4.)