A295568 Irregular triangle, read by rows: the Catalan generating tree, read from left to right, row by row, starting at the root.

2, 2, 3, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 6, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 6

Offset

1,1

Comments

Row n has Catalan(n) terms.

The rows converge to A076050.

Links

Rémy Sigrist, Rows n = 1..10 of triangle, flattened

D. Kremer, Permutations with forbidden subsequences and a generalized Schröder number, Discrete Math. 218 (2000) 121-130.

Julian West, Generating trees and the Catalan and Schröder numbers, Discrete Math. 146 (1995), 247-262.

Julian West, Generating trees and forbidden subsequences, Discrete Math., 157 (1996), 363-374.

Example

The triangle starts with a root node (at level 1) labeled 2; thereafter every node labeled k has k children at the next level whose labels are 2, 3, 4, ..., k, k+1.
Rows 1, 2, 3, 4, 5, and part of 6 are:
2,
2, 3,
2, 3, 2, 3, 4,
2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5,
2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 6,
2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 6, ...
...

Crossrefs

Cf. A000108, A076050, A295569.

Sequence in context: A331921 A185816 A324901 * A099427 A059964 A308050

Adjacent sequences: A295565 A295566 A295567 * A295569 A295570 A295571

Keyword

nonn,tabf

Author

N. J. A. Sloane, Nov 29 2017

Status

approved