A177543 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up, down.

1, 1, 2, 6, 24, 120, 720, 4768, 35968, 312064, 3004160, 31764480, 365798400, 4555499520, 61232590848, 882227765248, 13547017240576, 221038858829824, 3818608204709888, 69637156745773056, 1336921845773107200, 26947721453843251200, 569023211226594803712

Offset

0,3

Links

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

Formula

a(n) ~ c * d^n * n!, where d = 0.9598365530271216889440240044515..., c = 1.2474579024498809739499621681... . - 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, 5, 1, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 2, 6, 2][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 24 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, 5, 1, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6, 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 *)

Crossrefs

Column k=42 of A242784.

Sequence in context: A152363 A152359 A152362 * A189842 A189271 A152366

Adjacent sequences: A177540 A177541 A177542 * A177544 A177545 A177546

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 24 2013

Status

approved