A322468 Numbers that are sums of consecutive tetrahedral numbers.

0, 1, 4, 5, 10, 14, 15, 20, 30, 34, 35, 55, 56, 65, 69, 70, 84, 91, 111, 120, 121, 125, 126, 140, 165, 175, 195, 204, 205, 209, 210, 220, 260, 285, 286, 295, 315, 325, 329, 330, 364, 369, 385, 425, 455, 460, 480, 490, 494, 495, 505, 506, 560, 589, 645, 650, 671, 680, 700

Offset: 1

Author

Ilya Gutkovskiy, Dec 09 2018

Keywords

• nonn

Examples

			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.
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..603
• Eric Weisstein's World of Mathematics, Tetrahedral Number

Crossrefs

Cf. A000292 (tetrahedral numbers, a subsequence), A000330 (subsequence), A006003 (subsequence), A005894 (subsequence).

Other sums of consecutive numbers: A034705 (squares), A034706 (triangular numbers), A322479 (square pyramidal numbers), A322610 (centered triangular numbers), A322611 (centered square numbers).

Programs

Mathematica

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 *)
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 *)