A177540 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, down.

1, 1, 2, 6, 24, 120, 720, 4908, 38208, 334368, 3248640, 34774112, 405758208, 5129918808, 69849531936, 1018876044528, 15854497560576, 262116761475488, 4588408779868800, 84784281517177940, 1649073291620014880, 33678805727832427224, 720569710852319474016

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 = 0.97251576612005359341988641793523250275..., c = 1.18354011206219905745522624899424386... . - 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, 4, 1, 3, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 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, 4, 1, 3, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 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=38 of A242784.

Sequence in context: A177539 A177546 A177544 * A068201 A189848 A189285

Adjacent sequences: A177537 A177538 A177539 * A177541 A177542 A177543

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

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

Status

approved