OFFSET
1,2
COMMENTS
Replacing "three" by "two" we get A001652.
Replacing "three" by "N" we get: {15} for N = 4 and 5, {2079} for N = 6 and no solutions for N >= 7. - J. B. M. Melissen.
t(a(n)) equals x*(x+1)*(x+2) for x = [0, 1, 4, 5, 9, 56, 636]_n. - Zak Seidov, Jun 21 2013
LINKS
S. P. Mohanty, Which triangular numbers are products of three consecutive integers?, Acta Mathematica Hungarica 1991, Volume 58, Issue 1-2, pp 31-36.
MATHEMATICA
(Sqrt[8#+1]-1)/2&/@Select[Table[n(n+1)(n+2), {n, 0, 23000}], OddQ[Sqrt[8#+1]]&] (* Harvey P. Dale, Jan 12 2023 *)
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
N. J. A. Sloane, Aug 29 2004
STATUS
approved