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 A322468 #29 Jun 05 2025 07:41:42
%S A322468 0,1,4,5,10,14,15,20,30,34,35,55,56,65,69,70,84,91,111,120,121,125,
%T A322468 126,140,165,175,195,204,205,209,210,220,260,285,286,295,315,325,329,
%U A322468 330,364,369,385,425,455,460,480,490,494,495,505,506,560,589,645,650,671,680,700
%N A322468 Numbers that are sums of consecutive tetrahedral numbers.
%H A322468 R. J. Mathar, <a href="/A322468/b322468.txt">Table of n, a(n) for n = 1..603</a>
%H A322468 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>
%e A322468 209 = sum_{k=2..7} A000292(k) so 209 is in the list. 295=sum_{k=5..8} A000292(k), so 295 is in the list.
%t A322468 tet[n_] := n (n + 1) (n + 2)/6; nMax = 700; t = {0}; Do[k = n; s = 0; While[s = s + tet[k]; s <= nMax, AppendTo[t, s]; k++], {n, (6*nMax)^(1/3) + 1}]; t = Union[t] (* _Amiram Eldar_, Dec 09 2018 after _T. D. Noe_ at A034705 *)
%t A322468 anmax = 1000; nmax = Floor[(6*anmax)^(1/3)] + 1; Select[Union[Flatten[Table[Sum[k*(k + 1)*(k + 2)/6, {k, i, j}], {i, 0, nmax}, {j, i, nmax}]]], # <= anmax &] (* _Vaclav Kotesovec_, Dec 21 2018 *)
%Y A322468 Cf. A000292 (tetrahedral numbers, a subsequence), A000330 (subsequence), A006003 (subsequence), A005894 (subsequence).
%Y A322468 Other sums of consecutive numbers: A034705 (squares), A034706 (triangular numbers), A322479 (square pyramidal numbers), A322610 (centered triangular numbers), A322611 (centered square numbers).
%K A322468 nonn
%O A322468 1,3
%A A322468 _Ilya Gutkovskiy_, Dec 09 2018