A177532 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, up, up.

1, 1, 2, 6, 24, 120, 701, 4774, 37128, 326089, 3184221, 34191983, 400308461, 5076257396, 69329710171, 1014612340743, 15838898430094, 262706269352374, 4613506518038420, 85520547931176984, 1668736482655334275, 34189755475407632542, 733851215342599413848

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) ~ c * d^n * n!, where d = 0.975638124670183802889377522566191208591041394..., c = 1.123281860028517266849117754708517961017398615... . - Vaclav Kotesovec, Jan 17 2015

Maple

b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
      add(b(u-j, o+j-1, [1, 1, 4, 1, 1][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 3, 3, 5, 6][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
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 + t < 6, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 1, 4, 1, 1}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 3, 3, 5, 6}[[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 *)

Crossrefs

Column k=27 of A242784.

Sequence in context: A189284 A274970 A177525 * A242573 A223034 A177530

Adjacent sequences: A177529 A177530 A177531 * A177533 A177534 A177535

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 21 2013

Status

approved