A177522 Number of permutations of 1..n avoiding adjacent step pattern up, up, down, down.

1, 1, 2, 6, 24, 114, 648, 4284, 32256, 273616, 2578352, 26725776, 302273664, 3703441104, 48865510848, 690823736064, 10417318281216, 166907223390976, 2831507368842752, 50703852290781696, 955742450175919104, 18916030525704006144, 392213482250102734848

Offset: 0

Author

R. H. Hardin, May 10 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..454

Crossrefs

Column k=12 of A242784.

Programs

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 *)

Formula

a(n) ~ c * d^n * n!, where d = 0.942475018599378010857210678432739023432859616925664352..., c = 1.284751954587372264742653082845227922651555734159194626... . - Vaclav Kotesovec, Aug 29 2014

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 07 2013

a(0)=1 from Alois P. Heinz, Apr 20 2022