

A001219


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


7




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 12, pp 3136.
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

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



