OFFSET
1,6
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
Rigoberto Flórez, José L. Ramírez, Fabio A. Velandia, and Diego Villamizar, Some Connections Between Restricted Dyck Paths, Polyominoes, and Non-Crossing Partitions, arXiv:2308.02059 [math.CO], 2023. See Table 1 p. 13.
FORMULA
a(n) = 1 if n <= 5; otherwise, Sum_{i=0..n-5} binomial(n-5,i)*a(i). Proved by R. J. Mathar in the Sequence Fans Mailing List.
EXAMPLE
Some solutions for n=15:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....0....0....1....1....0....1....0....1....1....1....0....1....1....1
..0....0....0....0....0....0....1....1....1....0....1....0....0....1....1....0
..1....1....0....1....1....1....1....1....0....1....1....1....1....1....1....0
..0....0....1....0....1....0....1....0....0....1....0....0....1....1....1....1
..1....0....1....1....0....1....1....1....1....1....0....0....0....1....1....0
..0....0....1....1....0....1....1....1....1....1....0....0....1....1....1....1
..0....1....0....0....1....1....1....2....1....0....1....0....1....2....0....1
..0....0....0....0....0....2....1....0....1....1....1....1....1....2....1....0
..0....1....1....1....0....2....1....1....0....0....0....1....1....0....0....0
..0....0....1....1....0....0....1....0....1....1....0....0....2....2....0....1
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 22 2012
STATUS
approved