OFFSET
0,3
COMMENTS
Also the number of tree-child networks with a maximal number n of reticulations nodes. - Michael Fuchs, Aug 05 2020
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..320
Cyril Banderier and Michael Wallner, Young tableaux with periodic walls: counting with the density method, Séminaire Lotharingien de Combinatoire XX, Proceedings of the 33rd Conference on Formal Power (2021) Article #YY.
Michael Fuchs, Enumeration and Stochastic Properties of Tree-Child Networks, National Chengchi Univ. (Taipei 2023).
Michael Fuchs, Guan-Ru Yu, and Louxin Zhang, On the Asymptotic Growth of the Number of Tree-Child Networks, arXiv:2003.08049 [math.CO], 2020.
FORMULA
a(n) = Sum_{m>=1} b_{n,m} if n>0. Here, b_{n,m} satisfies b_{n,m}=(2*n+m-2)*Sum_{k=1..m} b_{n-1,k} for n>=2 and 1<=m<=n with initial conditions b_{n,m}=0 for n<m and b_{1,1}=1. - Michael Fuchs, Aug 05 2020
EXAMPLE
a(0) = 1: the empty word.
a(1) = 1: aaa.
a(2) = 7: aaabbb, aababb, aabbab, abaabb, ababab, baaabb, baabab.
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 23 2012
STATUS
approved