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A295568
Irregular triangle, read by rows: the Catalan generating tree, read from left to right, row by row, starting at the root.
2
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
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
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Nov 29 2017
STATUS
approved