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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

%I

%S 2,19,74,113,197,482,1162,1959,1937,5644,6061,10788,12772,17624,19401,

%T 16503,29195,25487,60881,63348,89133

%N 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.

%C i values are A054208 and k values are A054210.

%e 2^3=8=binomial(2+2,3)+binomial(2+2,3); 11^3=1331=binomial(19+2,3)+binomial(3,3);

%t (* 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-Fran├žois Alcover_, Sep 11 2012 *)

%Y Cf. A054208, A054210.

%K nonn,nice

%O 0,1

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 31 2000

%E More terms from _Sascha Kurz_, Mar 22 2002

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Last modified June 25 06:20 EDT 2021. Contains 345452 sequences. (Running on oeis4.)