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 A224421 #19 May 31 2024 14:04:01
%S A224421 0,1,3,8,20,34
%N A224421 The indices of tetrahedral numbers that are also triangular.
%H A224421 E. T. Avanesov, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa12/aa12128.pdf">Solution of a problem on figurate numbers</a> (in Russian), Acta Arith. 12 1966/1967 pages 409-420.
%e A224421 The eighth tetrahedral number is 120, which is also a triangular number. Hence, 8 belongs to the sequence.
%t A224421 Select[Table[{n,(n(n+1)(n+2))/6},{n,0,35}],OddQ[Sqrt[1+8#[[2]]]]&][[;;,1]] (* _Harvey P. Dale_, May 31 2024 *)
%o A224421 (PARI) for(n=0,34,if(ispolygonal(n*(n+1)*(n+2)/6,3),print1(n", "))) \\ _Charles R Greathouse IV_, Apr 07 2013
%Y A224421 Cf. A027568, A102349.
%K A224421 nonn,full,fini
%O A224421 0,3
%A A224421 _Tanya Khovanova_, Apr 06 2013