Table 1. Sequences enumerating the (1,2) avoidance classes for Catalan words
τ
Sequence
Reference
1-11
1,1,1,3,6,15,39,102,275,754
Theorem 5.15
1-12
A000045 in [11]
Observation 6.2
1-21
1,1,1,1,1,1,1,1,1,1
Observation 6.1
1-22
A001006
Theorem 3.3
1-23
1,1,2,5,13,33,82,202,497,1224
Proposition 2.2 and Theorem 5.4
1-32
A000325
Observation 6.2
2-11
1,1,2,4,10,26,71,199,570,1659
Open
2-12
1,1,2,4,9,22,56,146,388,1047
Proposition 2.2 and Theorem 4.3
2-13
1,1,2,5,13,34,91,248,685,1911
Proposition 2.2 and Theorem 5.8
2-21
A011782
Observation 6.2
2-31
A000108
Observation 6.1
3-12
1,1,2,5,14,41,123,376,1167,3665
Proposition 2.2 and Theorem 4.5
3-21
A001519
Observation 6.2
Toufik Mansour et al. Avoidance of Type (1,2) Patterns by Catalan Words. Turkish Journal of Analysis and Number
Theory, 2017, Vol. 5, No. 3, 101-116. doi:10.12691/tjant-5-3-4
© The Author(s) 2015. Published by Science and Education Publishing.