A210542 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 5 times

1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 65, 138, 315, 782, 2090, 5885, 17112, 50743, 152705, 466760, 1455562, 4658963, 15392116, 52663709, 186632887, 683133153, 2570929570, 9900731604, 38864321047, 155126476313, 629028834312, 2592051975917

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

Column 5 of A210545.

Sequence in context: A084637 A100137 A325917 * A141366 A049142 A367661

Adjacent sequences: A210539 A210540 A210541 * A210543 A210544 A210545

Keyword

nonn

Author

R. H. Hardin, Mar 22 2012

Status

approved