A054210 - OEIS

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.

%I #21 May 07 2024 12:08:21

%S 2,1,49,54,19,266,308,197,1834,2354,1562,8812,10988,998,1959,14706,

%T 15089,23758,3005,26023,39490,23156,93724,19401,123338,69550,170653,

%U 299009,303139,574368,192059,1029696

%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 k values.

%C i values are A054208 and j values are A054209.

%e 2^3 = 8 = binomial(2+2,3) + binomial(2+2,3).

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

%t (* This is just a re-computation from A054208 *)

%t A054208 = Cases[Import["https://oeis.org/A054208/b054208.txt", "Table"], {_, _}][[All, 2]];

%t 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 }];

%t A054210 = ijk[[All, 3]] (* _Jean-François Alcover_, May 07 2024 *)

%Y Cf. A054208, A054209.

%K nonn,nice,more

%O 0,1

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

%E More terms from _Sascha Kurz_, Mar 22 2002

%E a(21)-a(26) from _Sean A. Irvine_, Jan 25 2022

%E a(27)-a(31) from _Jean-François Alcover_, May 07 2024