A175492 -id:A175492 - cp's OEIS frontend

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

Original entry on oeis.org

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

Offset: 1

Alex Ratushnyak, Mar 15 2013

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

Cf. A000292, A216269, A175492.

Cf. A003556 (both square and tetrahedral).

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

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 *)

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 */

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=' ')

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