A216268 Tetrahedral numbers of the form k^2 - 1.

0, 35, 120, 2024, 2600, 43680, 435730689800

Offset

1,2

Comments

This sequence is finite by Siegel's theorem on integral points. The next term, if it exists, is greater than 10^35. - David Radcliffe, Jan 01 2024

Links

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

Maple

select(t -> issqr(t+1), [seq(i*(i+1)*(i+2)/6, i=0..10^6)]); # Robert Israel, Jan 02 2024

Mathematica

t = {}; Do[tet = n (n + 1) (n + 2)/6; If[IntegerQ[Sqrt[tet + 1]], AppendTo[t, tet]], {n, 0, 100000}]; t (* T. D. Noe, Mar 18 2013 *)

Prog

(Python)
import math
for i in range(1<<33):
    t = i*(i+1)*(i+2)//6 + 1
    sr = math.isqrt(t)
    if sr*sr == t:
        print (t-1, sep=' ')
(PARI)
A000292(n) = n*(n+1)*(n+2)\6;
for(n=0, 10^9, t=A000292(n); if (issquare(t+1), print1(t, ", ") ) );
/* Joerg Arndt, Mar 16 2013 */

Crossrefs

Cf. A000292, A216269, A175492.

Cf. A003556 (both square and tetrahedral).

Sequence in context: A337233 A230214 A284876 * A098218 A247679 A344013

Adjacent sequences: A216265 A216266 A216267 * A216269 A216270 A216271

Keyword

nonn,more,fini

Author

Alex Ratushnyak, Mar 15 2013

Status

approved