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A001219 Triangular numbers of form a(a+1)(a+2). 7
0, 6, 120, 210, 990, 185136, 258474216 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified December 14 09:20 EST 2018. Contains 318091 sequences. (Running on oeis4.)