A177548 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, down, down, down.

1, 1, 2, 6, 24, 120, 720, 5025, 40080, 359640, 3585600, 39322800, 470448000, 6097392939, 85106238492, 1272746220570, 20302567148160, 344103461618400, 6175195781293440, 116975122363277289, 2332451810975205960, 48833870901559002540, 1071107370496773577440

Offset: 0

Author

R. H. Hardin, May 10 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..175

Crossrefs

Columns k=48,60 of A242784.

Programs

Maple

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
      add(b(u-j, o+j-1, [1, 1, 4, 5, 6, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 3, 3, 2, 2, 2][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 23 2013

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 1, 4, 5, 6, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 3, 3, 2, 2, 2}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n * n!, where d = 0.99698626702423025316812958090212389097043667361318991688710688185165..., c = 1.018367520648807878150063272123153629935889863110044893080319840979... . - Vaclav Kotesovec, Jan 17 2015

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 23 2013