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

1,3

Links

Table of n, a(n) for n=1..59.

Eric Weisstein's World of Mathematics, Tetrahedral Number

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 *)

Crossrefs

Cf. A000292 (tetrahedral numbers).

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

Sequence in context: A357865 A366864 A322610 * A116930 A073119 A002257

Adjacent sequences: A322465 A322466 A322467 * A322469 A322470 A322471

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 09 2018

Status

approved