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

Author

N. J. A. Sloane, Nov 29 2017

Keywords

• nonn
• tabf

Comments

Row n has Catalan(n) terms.

The rows converge to A076050.

Examples

			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, ...
...
		

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.

Crossrefs

Cf. A000108, A076050, A295569.