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 A210540 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 3 times. 9
 1, 1, 1, 1, 2, 4, 8, 17, 40, 104, 291, 857, 2634, 8455, 28424, 100117, 368465, 1410903, 5599073, 22968514, 97267342, 424927846, 1913764155, 8877181958, 42358589064, 207639979365, 1044360973987, 5384167878948, 28429186870051, 153638182314504, 849295001319211 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..700 (terms n = 1..210 from R. H. Hardin) 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<=3 else Sum_{i=0..n-3} binomial(n-3,i)*a(i). Proved by R. J. Mathar in the Sequence Fans Mailing List. EXAMPLE Some solutions for n=11 ..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....0....1....1....1....0....1....1....1....1....1....1....1....1....0 ..0....1....1....0....1....1....1....0....1....0....0....0....1....1....0....0 ..1....1....0....1....0....1....1....0....1....1....0....1....1....1....1....1 ..1....0....1....1....1....0....1....0....2....1....0....1....2....2....0....0 ..2....2....0....2....2....2....0....0....0....1....1....0....1....2....0....0 ..2....0....0....2....2....2....0....1....1....0....1....1....2....2....0....1 ..2....1....0....1....0....1....2....0....1....0....2....0....2....2....1....1 ..3....1....1....0....2....2....0....1....0....2....1....0....2....0....2....1 CROSSREFS Column 3 of A210545. Sequence in context: A373353 A304970 A090375 * A332398 A307555 A104879 Adjacent sequences: A210537 A210538 A210539 * A210541 A210542 A210543 KEYWORD nonn AUTHOR R. H. Hardin, Mar 22 2012 EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Apr 24 2023 STATUS approved

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Last modified September 7 23:52 EDT 2024. Contains 375749 sequences. (Running on oeis4.)