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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 R. H. Hardin, Table of n, a(n) for n = 1..9999 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 Adjacent sequences: A210542 A210543 A210544 * A210546 A210547 A210548 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 22 2012 STATUS approved

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Last modified September 10 09:32 EDT 2024. Contains 375786 sequences. (Running on oeis4.)