A001219 Triangular numbers of form a(a+1)(a+2).

0, 6, 120, 210, 990, 185136, 258474216

Offset

1,2

References

R. K. Guy, Unsolved Problems in Number Theory, D3.

Links

Table of n, a(n) for n=1..7.

S. P. Mohanty, Which triangular numbers are products of three consecutive integers?, Acta Mathematica Hungarica 1991, Volume 58, Issue 1-2, pp 31-36.

Eric Weisstein's World of Mathematics, Triangular Number.

Formula

a(n) = A000217(A097571(n)). - Michel Marcus, Jan 14 2015

Maple

count:= 0:
for a from 0 to 637 do
  p:= a*(a+1)*(a+2);
  if issqr(1+8*p) then
    count:= count+1;
    A[count]:= p;
  fi
od:
seq(A[i], i=1..count); # Robert Israel, Jan 14 2015

Mathematica

Select[Times @@@ Partition[Range[0, 700], 3, 1], OddQ[ Sqrt[ 8 # + 1]] &] (* Harvey P. Dale, Nov 04 2017 *)

Crossrefs

Cf. A000217, A097571.

Sequence in context: A117063 A178911 A227027 * A224303 A076233 A066581

Adjacent sequences: A001216 A001217 A001218 * A001220 A001221 A001222

Keyword

nonn,fini,full

Author

N. J. A. Sloane

Status

approved