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A351846
Irregular triangle read by rows: T(n,k), n >= 0, k >= 0, in which n appears 4*n + 1 times in row n.
7
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.
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.
Sequence in context: A242306 A245636 A171622 * A111858 A111856 A111857
KEYWORD
nonn,tabf,easy
AUTHOR
Omar E. Pol, Feb 21 2022
STATUS
approved