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A210545 T(n,k) = number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least k times. 6
1, 1, 2, 1, 1, 5, 1, 1, 2, 15, 1, 1, 1, 4, 52, 1, 1, 1, 2, 9, 203, 1, 1, 1, 1, 4, 23, 877, 1, 1, 1, 1, 2, 8, 65, 4140, 1, 1, 1, 1, 1, 4, 17, 199, 21147, 1, 1, 1, 1, 1, 2, 8, 40, 654, 115975, 1, 1, 1, 1, 1, 1, 4, 16, 104, 2296, 678570, 1, 1, 1, 1, 1, 1, 2, 8, 33, 291, 8569, 4213597, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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
T(n,k)=1 if n<=k else Sum_{i=0..n-k} binomial(n-k,i)*T(i,k). Proved by R. J. Mathar in the Sequence Fans Mailing List.
EXAMPLE
Some solutions for n=13 k=4
..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....1....1....1....0....0....1....0....0....1....1....0....1....1
..0....0....1....1....1....1....1....0....0....0....1....1....0....1....1....0
..1....0....0....1....1....1....0....1....1....0....0....0....0....1....1....0
..0....1....1....0....1....1....0....1....0....0....1....0....0....1....1....1
..1....1....0....0....1....2....1....1....0....1....1....0....0....1....2....1
..0....1....0....1....0....1....1....1....1....0....1....1....1....1....2....1
..0....1....0....2....1....0....0....1....1....0....2....0....1....1....2....1
..1....2....0....1....1....0....1....0....0....1....1....0....0....2....1....0
..0....2....1....0....2....0....0....0....2....1....2....1....0....0....0....1
Table starts
..........1.......1......1.....1....1...1...1
..........2.......1......1.....1....1...1...1
..........5.......2......1.....1....1...1...1
.........15.......4......2.....1....1...1...1
.........52.......9......4.....2....1...1...1
........203......23......8.....4....2...1...1
........877......65.....17.....8....4...2...1
.......4140.....199.....40....16....8...4...2
......21147.....654....104....33...16...8...4
.....115975....2296....291....73...32..16...8
.....678570....8569....857...177...65..32..16
....4213597...33825...2634...467..138..64..32
...27644437..140581...8455..1309..315.129..64
..190899322..612933..28424..3813..782.267.128
.1382958545.2795182.100117.11409.2090.582.257
CROSSREFS
Cf. A000110 (column 1), A007476 (column 2), A210540 (column 3).
Sequence in context: A169950 A088347 A069568 * A141323 A210876 A174785
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 22 2012
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)