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 A054210 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 k values. 3
 2, 1, 49, 54, 19, 266, 308, 197, 1834, 2354, 1562, 8812, 10988, 998, 1959, 14706, 15089, 23758, 3005, 26023, 39490 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS i values are A054208 and j values are A054209. 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 }]; A054210 = ijk[[All, 3]] (* Jean-François Alcover, Sep 11 2012 *) CROSSREFS Cf. A054208, A054209. Sequence in context: A255856 A037056 A109347 * A225778 A271442 A092650 Adjacent sequences:  A054207 A054208 A054209 * A054211 A054212 A054213 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 June 15 22:06 EDT 2021. Contains 345053 sequences. (Running on oeis4.)