A177545 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, down, down.

1, 1, 2, 6, 24, 120, 720, 4929, 38544, 338904, 3309120, 35521200, 415704960, 5271197205, 71977504692, 1053008012790, 16431803844480, 272435676775200, 4782657847248000, 88624515772410633, 1728678866577622920, 35404942557640528620, 759655818204633900000

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..190

Formula

a(n) ~ c * d^n * n!, where d = 0.9752820884477652193970997660966130503977714987577677..., c = 1.1721546677937404500752065441275892023818795500231... . - Vaclav Kotesovec, Jan 17 2015

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, 3, 1, 3, 6, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 5, 2, 4][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 22 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, 3, 1, 3, 6, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 2, 4}[[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

Columns k=44,50 of A242784.

Sequence in context: A068201 A189848 A189285 * A177538 A177550 A177536

Adjacent sequences: A177542 A177543 A177544 * A177546 A177547 A177548

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

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

Status

approved