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.

2, 1, 49, 54, 19, 266, 308, 197, 1834, 2354, 1562, 8812, 10988, 998, 1959, 14706, 15089, 23758, 3005, 26023, 39490, 23156, 93724, 19401, 123338, 69550, 170653, 299009, 303139, 574368, 192059, 1029696

Offset

0,1

Comments

i values are A054208 and j values are A054209.

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 }];
A054210 = ijk[[All, 3]] (* Jean-François Alcover, May 07 2024 *)

Crossrefs

Cf. A054208, A054209.

Sequence in context: A037056 A358857 A109347 * A225778 A271442 A092650

Adjacent sequences: A054207 A054208 A054209 * A054211 A054212 A054213

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