A351846 Irregular triangle read by rows: T(n,k), n >= 0, k >= 0, in which n appears 4*n + 1 times in row n.

0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset

0,7

Comments

a(n) is the number of hexagonal numbers A000384 less than or equal to n, not counting 0 as hexagonal.

This sequence is related to hexagonal numbers as A003056 is related to triangular numbers (or generalized hexagonal numbers) A000217.

Links

Table of n, a(n) for n=0..90.

Formula

a(n) = floor((sqrt(8*n + 1) + 1)/4). - Ridouane Oudra, Apr 09 2023

Example

Triangle begins:
  0;
  1, 1, 1, 1, 1;
  2, 2, 2, 2, 2, 2, 2, 2, 2;
  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3;
  4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4;
  5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5;
  6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6;
  ...

Mathematica

Table[PadRight[{}, 4n+1, n], {n, 0, 7}]//Flatten (* Harvey P. Dale, Jun 04 2023 *)

Crossrefs

Row sums give A007742.

Row n has length A016813(n).

Column 0 gives A001477, the same as the right border.

Nonzero terms give the row lengths of the triangles A347263, A347529, A351819, A351824, A352269, A352499.

Cf. A000217, A000384, A003056.

Sequence in context: A242306 A245636 A171622 * A111858 A111856 A111857

Adjacent sequences: A351843 A351844 A351845 * A351847 A351848 A351849

Keyword

nonn,tabf,easy

Author

Omar E. Pol, Feb 21 2022

Status

approved