A177524 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down.

1, 1, 2, 6, 24, 120, 715, 4970, 39480, 352800, 3502800, 38255900, 455795100, 5883052500, 81774966000, 1217871018000, 19346879737625, 326549862671250, 5835951345093750, 110091785625495000, 2186122850020215000, 45580964489553559375, 995625115672520581250

Offset: 0

Author

R. H. Hardin, May 10 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..170

Crossrefs

Columns k=16,30 of A242784.

Programs

Maple

b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
      add(b(u-j, o+j-1, `if`(t=1, 1, t+1)), j=1..u)+
      add(b(u+j-1, o-j, 2), j=1..o)))
    end:
a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 21 2013

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o == 0, 1,
     Sum[b[u - j, o + j - 1, If[t == 1, 1, t + 1]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, 2], {j, 1, o}]]];
a[n_] := If[n == 0, 1, Sum[b[j - 1, n - j, 1], {j, 1, n}]];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 20 2022, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n * n!, where d = 0.9928637443921790380857377558103269268777241137790934589694993..., c = 1.0369478195304845650491426260146999487076420703190374702807322... . - Vaclav Kotesovec, Aug 29 2014

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 20 2013