This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A216268 #36 Jul 04 2025 17:45:33
%S A216268 0,35,120,2024,2600,43680,435730689800
%N A216268 Tetrahedral numbers of the form k^2 - 1.
%C A216268 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
%p A216268 select(t -> issqr(t+1), [seq(i*(i+1)*(i+2)/6, i=0..10^6)]); # _Robert Israel_, Jan 02 2024
%t A216268 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 *)
%o A216268 (Python)
%o A216268 import math
%o A216268 for i in range(1<<33):
%o A216268 t = i*(i+1)*(i+2)//6 + 1
%o A216268 sr = math.isqrt(t)
%o A216268 if sr*sr == t:
%o A216268 print (t-1, sep=' ')
%o A216268 (PARI)
%o A216268 A000292(n) = n*(n+1)*(n+2)\6;
%o A216268 for(n=0,10^9, t=A000292(n); if (issquare(t+1), print1(t,", ") ) );
%o A216268 /* _Joerg Arndt_, Mar 16 2013 */
%Y A216268 Cf. A000292, A216269, A175492.
%Y A216268 Cf. A003556 (both square and tetrahedral).
%K A216268 nonn,more,fini
%O A216268 1,2
%A A216268 _Alex Ratushnyak_, Mar 15 2013