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 A177522 Number of permutations of 1..n avoiding adjacent step pattern up, up, down, down. 2
 1, 1, 2, 6, 24, 114, 648, 4284, 32256, 273616, 2578352, 26725776, 302273664, 3703441104, 48865510848, 690823736064, 10417318281216, 166907223390976, 2831507368842752, 50703852290781696, 955742450175919104, 18916030525704006144, 392213482250102734848 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..454 FORMULA a(n) ~ c * d^n * n!, where d = 0.942475018599378010857210678432739023432859616925664352..., c = 1.284751954587372264742653082845227922651555734159194626... . - Vaclav Kotesovec, Aug 29 2014 MAPLE b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(b(u+j-1, o-j, `if`(t in [0, 3], 1, 2)), j=1..o)+`if`(t<3, add(b(u-j, o+j-1, `if`(t=2, 3, 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[MemberQ[{0, 3}, t], 1, 2]], {j, 1, o}] + If[t<3, Sum[b[u-j, o+j-1, If[t == 2, 3, 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=12 of A242784. Sequence in context: A068199 A189846 A189283 * A216717 A174072 A224255 Adjacent sequences: A177519 A177520 A177521 * A177523 A177524 A177525 KEYWORD nonn AUTHOR R. H. Hardin, May 10 2010 EXTENSIONS a(17)-a(22) from Alois P. Heinz, Oct 07 2013 a(0)=1 from Alois P. Heinz, Apr 20 2022 STATUS approved

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Last modified June 8 00:22 EDT 2023. Contains 363157 sequences. (Running on oeis4.)