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A295569 Irregular triangle, read by rows: the Schroeder generating tree, read from left to right, row by row, starting at the root. 3
2, 3, 3, 3, 4, 4, 3, 4, 4, 3, 4, 4, 3, 4, 5, 5, 3, 4, 5, 5, 3, 4, 4, 3, 4, 5, 5, 3, 4, 5, 5, 3, 4, 4, 3, 4, 5, 5, 3, 4, 5, 5, 3, 4, 4, 3, 4, 5, 5, 3, 4, 5, 6, 6, 3, 4, 5, 6, 6, 3, 4, 4, 3, 4, 5, 5, 3, 4, 5, 6, 6, 3, 4, 5, 6, 6, 3, 4, 4, 3, 4, 5, 5, 3, 4, 5, 5, 3, 4, 4, 3, 4, 5, 5, 3, 4, 5, 6, 6, 3, 4, 5, 6, 6, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row n has A006318(n-1) terms (these are the large Schroeder numbers).

The limiting sequence of the rows is A295570.

LINKS

Rémy Sigrist, Rows n = 1..9 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 3, 4, ..., k, k+1, k+1.

Rows 1, 2, 3, 4, and part of 5 are:

2,

3,3,

3,4,4,3,4,4,

3,4,4,3,4,5,5,3,4,5,5,3,4,4,3,4,5,5,3,4,5,5,

3,4,4,3,4,5,5,3,4,5,5,3,4,4,3,4,5,5,3,4,5,6,6,3,4,5,6,6,...

...

MAPLE

with(ListTools);

psi:=proc(S)

Flatten(subs( {2=[3, 3], 3=[3, 4, 4], 4=[3, 4, 5, 5], 5=[3, 4, 5, 6, 6], 6=[3, 4, 5, 6, 7, 7], 7=[3, 4, 5, 6, 7, 8, 8]}, S)); # This will only work for the first 7 generations. For further generations, extend the "subs" command

end;

S:=[2];

for n from 1 to 6 do S:=psi(S): od:

S;

CROSSREFS

Cf. A006318, A295568, A295570.

Sequence in context: A322974 A326201 A342625 * A129574 A323466 A130193

Adjacent sequences:  A295566 A295567 A295568 * A295570 A295571 A295572

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Nov 29 2017

STATUS

approved

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Last modified May 22 10:52 EDT 2022. Contains 353949 sequences. (Running on oeis4.)