A210541 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 4 times.

1, 1, 1, 1, 2, 4, 8, 16, 33, 73, 177, 467, 1309, 3813, 11409, 34999, 110510, 361194, 1226930, 4334048, 15877297, 60049447, 233426007, 929616461, 3786970033, 15777120457, 67260334185, 293617319221, 1312868943154, 6010792180952

Offset: 1

Author

R. H. Hardin, Mar 22 2012

Keywords

• nonn

Comments

Column 4 of A210545

Examples

			Some solutions for n=13
..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....1....1....0....1....1....1....0....1....1....0....0....1....0....0....1
..1....1....1....1....1....0....1....0....1....1....1....1....0....1....1....1
..0....1....0....0....1....0....1....0....0....0....0....1....0....0....1....0
..0....1....1....1....1....1....0....1....1....1....1....0....1....1....1....1
..1....2....1....0....0....1....1....1....1....1....0....0....1....1....1....0
..1....0....2....1....2....1....0....0....2....0....0....0....0....1....0....0
..0....1....1....1....2....2....1....1....1....0....0....1....0....2....2....1
..1....0....2....0....1....2....1....1....0....1....0....1....1....0....1....1
..2....0....1....2....1....0....2....2....2....0....0....1....2....0....2....0
		

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<=4 else sum{i=0..n-4}(binomial(n-4,i)*a(i)). Proved by R. J. Mathar in the Sequence Fans Mailing List.