A177536 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up, down.

1, 1, 2, 6, 24, 120, 720, 4962, 39072, 346032, 3404160, 36853442, 435133488, 5566069380, 76676528112, 1131700250442, 17817052536384, 298034349244128, 5278625637077376, 98686282426953080, 1942087278998014400, 40130098178033129036, 868710371909527352944

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 = 0.983970585738736307495769238852152954976022611246..., c = 1.1028129540167952253429967393297373345979852081... . - 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, 5, 1, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 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, 4, 5, 1, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 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=34,46 of A242784.

Sequence in context: A177545 A177538 A177550 * A177549 A177542 A177537

Adjacent sequences: A177533 A177534 A177535 * A177537 A177538 A177539

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

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

Status

approved