login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 11 21:15 EST 2017. Contains 295919 sequences.