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 A177477 Number of permutations of 1..n avoiding adjacent step pattern up, down, up. 9
 1, 1, 2, 6, 19, 70, 331, 1863, 11637, 81110, 635550, 5495339, 51590494, 524043395, 5743546943, 67478821537, 844983073638, 11240221721390, 158365579448315, 2355375055596386, 36870671943986643, 606008531691619131, 10435226671431973345, 187860338952519968538 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Suppose a < b, c < b, and c < d. To avoid abcd means not to have four consecutive letters such that the first letter is less than the second one, the third letter is less than the second one, and the third letter is less than the last one. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..468 Sergey Kitaev, Introduction to partially ordered patterns, Discrete Applied Mathematics 155 (2007), 929-944. FORMULA a(n) ~ c * d^n * n!, where d = A245758 = 0.7827041801715217018447074977..., c = 2.035127405829990832658061124449458067... . - Vaclav Kotesovec, Aug 22 2014 MAPLE b:= proc(u, o, t) option remember; `if`(u+o=0, 1,        add(b(u-j, o+j-1, [1, 3, 1][t]), j=1..u)+       `if`(t=3, 0, add(b(u+j-1, o-j, 2), j=1..o)))     end: a:= n-> b(n, 0, 1): seq(a(n), n=0..25);  # Alois P. Heinz, Mar 10 2020 MATHEMATICA b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1,      Sum[b[u - j, o + j - 1, {1, 3, 1}[[t]]], {j, 1, u}] +      If[t == 3, 0, Sum[b[u + j - 1, o - j, 2], {j, 1, o}]]]; a[n_] := b[n, 0, 1]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Mar 08 2022, after Alois P. Heinz *) CROSSREFS Column k=0 of A227884. Column k=5 of A242784. Cf. A227883, A245758. Sequence in context: A150114 A199128 A150115 * A150116 A150117 A038392 Adjacent sequences:  A177474 A177475 A177476 * A177478 A177479 A177480 KEYWORD nonn AUTHOR Submitted independently by Signy Olafsdottir (signy06(AT)ru.is), May 09 2010 (9 terms) and R. H. Hardin, May 10 2010 (17 terms) EXTENSIONS a(18)-a(23) from Alois P. Heinz, Oct 06 2013 a(0)=1 prepended by Alois P. Heinz, Mar 10 2020 STATUS approved

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Last modified September 26 08:20 EDT 2022. Contains 356993 sequences. (Running on oeis4.)