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 A177520 Number of permutations of 1..n avoiding adjacent step pattern up, down, up, down. 3
 1, 1, 2, 6, 24, 104, 528, 3296, 23168, 179712, 1573632, 15207424, 158880768, 1801996288, 22088716288, 289379395584, 4040899657728, 60045059489792, 944460646318080, 15670973219667968, 273813250221277184, 5024207327266603008, 96554813072964845568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..460 FORMULA a(n) ~ c * d^n * n!, where d = 0.87361286073825385348141673848..., c = 1.678751353034864037734331900009... . - Vaclav Kotesovec, Aug 28 2014 MAPLE b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(b(u+j-1, o-j, `if`(t=2, 3, 1)), j=1..o) +`if`(t<3, add(b(u-j, o+j-1, `if`(t=1, 2, 0)), j=1..u), 0)) end: a:= n-> b(n, 0, 0): seq(a(n), n=0..30); # Alois P. Heinz, Oct 07 2013 MATHEMATICA b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Sum[b[u + j - 1, o - j, If[t == 2, 3, 1]], {j, 1, o}] + If[t < 3, Sum[b[u - j, o + j - 1, If[t == 1, 2, 0]], {j, 1, u}], 0]]; a[n_] := b[n, 0, 0]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Apr 20 2022, after Alois P. Heinz *) CROSSREFS Column k=0 of A230797. Column k=10 of A242784. Sequence in context: A230797 A128652 A152316 * A152326 A152330 A152319 Adjacent sequences: A177517 A177518 A177519 * A177521 A177522 A177523 KEYWORD nonn AUTHOR R. H. Hardin, May 10 2010 EXTENSIONS a(17)-a(22) from Alois P. Heinz, Oct 07 2013 STATUS approved

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Last modified September 29 02:15 EDT 2023. Contains 365747 sequences. (Running on oeis4.)