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.

2, 19, 74, 113, 197, 482, 1162, 1959, 1937, 5644, 6061, 10788, 12772, 17624, 19401, 16503, 29195, 25487, 60881, 63348, 89133, 114519, 140524, 192059, 214754, 262224, 286321, 335103, 904043, 1190328, 1901197, 1833590

Offset

0,1

Comments

i values are A054208 and k values are A054210.

Links

Table of n, a(n) for n=0..31.

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 = Cases[Import["https://oeis.org/A054208/b054208.txt", "Table"], {_, _}][[All, 2]];
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, May 07 2024 *)

Crossrefs

Cf. A054208, A054210.

Sequence in context: A024389 A110050 A219121 * A256112 A272053 A317274

Adjacent sequences: A054206 A054207 A054208 * A054210 A054211 A054212

Keyword

nonn,nice,more

Author

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

Extensions

More terms from Sascha Kurz, Mar 22 2002

a(21)-a(26) from Sean A. Irvine, Jan 25 2022

a(27)-a(31) from Jean-François Alcover, May 07 2024

Status

approved