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

Author

R. H. Hardin, Mar 22 2012

Keywords

• nonn

Examples

			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
		

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.

Crossrefs

Column 5 of A210545.

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.