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

1,5

Comments

Column 4 of A210545

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.

Example

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

Crossrefs

Sequence in context: A084636 A352044 A161869 * A275545 A273972 A275443

Adjacent sequences: A210538 A210539 A210540 * A210542 A210543 A210544

Keyword

nonn

Author

R. H. Hardin, Mar 22 2012

Status

approved