A210540 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 3 times.

1, 1, 1, 1, 2, 4, 8, 17, 40, 104, 291, 857, 2634, 8455, 28424, 100117, 368465, 1410903, 5599073, 22968514, 97267342, 424927846, 1913764155, 8877181958, 42358589064, 207639979365, 1044360973987, 5384167878948, 28429186870051, 153638182314504, 849295001319211

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..700 (terms n = 1..210 from R. H. Hardin)

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<=3 else Sum_{i=0..n-3} binomial(n-3,i)*a(i). Proved by R. J. Mathar in the Sequence Fans Mailing List.

Example

Some solutions for n=11
..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....1....0....1....1....1....0....1....1....1....1....1....1....1....1....0
..0....1....1....0....1....1....1....0....1....0....0....0....1....1....0....0
..1....1....0....1....0....1....1....0....1....1....0....1....1....1....1....1
..1....0....1....1....1....0....1....0....2....1....0....1....2....2....0....0
..2....2....0....2....2....2....0....0....0....1....1....0....1....2....0....0
..2....0....0....2....2....2....0....1....1....0....1....1....2....2....0....1
..2....1....0....1....0....1....2....0....1....0....2....0....2....2....1....1
..3....1....1....0....2....2....0....1....0....2....1....0....2....0....2....1

Crossrefs

Column 3 of A210545.

Sequence in context: A373353 A304970 A090375 * A332398 A307555 A104879

Adjacent sequences: A210537 A210538 A210539 * A210541 A210542 A210543

Keyword

nonn

Author

R. H. Hardin, Mar 22 2012

Extensions

a(0)=1 prepended by Alois P. Heinz, Apr 24 2023

Status

approved