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%I #21 Jan 01 2024 18:56:39
%S 0,6,120,210,990,185136,258474216
%N Triangular numbers of form a(a+1)(a+2).
%D R. K. Guy, Unsolved Problems in Number Theory, D3.
%H S. P. Mohanty, <a href="http://dx.doi.org/10.1007/BF01903544">Which triangular numbers are products of three consecutive integers?</a>, Acta Mathematica Hungarica 1991, Volume 58, Issue 1-2, pp 31-36.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularNumber.html">Triangular Number.</a>
%F a(n) = A000217(A097571(n)). - _Michel Marcus_, Jan 14 2015
%p count:= 0:
%p for a from 0 to 637 do
%p p:= a*(a+1)*(a+2);
%p if issqr(1+8*p) then
%p count:= count+1;
%p A[count]:= p;
%p fi
%p od:
%p seq(A[i],i=1..count); # _Robert Israel_, Jan 14 2015
%t Select[Times @@@ Partition[Range[0, 700], 3, 1], OddQ[ Sqrt[ 8 # + 1]] &] (* _Harvey P. Dale_, Nov 04 2017 *)
%Y Cf. A000217, A097571.
%K nonn,fini,full
%O 1,2
%A _N. J. A. Sloane_
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