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

Author

Omar E. Pol, Feb 21 2022

Keywords

• nonn
• tabf
• easy

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.

Examples

			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;
  ...
		

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.

Programs

Mathematica

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

Formula

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