A177538 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down, down.

1, 1, 2, 6, 24, 120, 720, 4941, 38736, 341496, 3354939, 36244098, 427006404, 5448087216, 74864913552, 1102353646680, 17314190063037, 288936154260522, 5105249306345502, 95216905474054011, 1869347069817467076, 38535066745735462848, 832195054189721911392

Offset: 0

Author

R. H. Hardin, May 10 2010

Keywords

• nonn

Links

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

Crossrefs

Columns k=36,54 of A242784.

Programs

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, 6, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 2, 2][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, 4, 1, 6, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 2, 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 *)

Formula

a(n) ~ c * d^n * n!, where d = 0.98162590771907099517875504406285427992737137228..., c = 1.1133866874983726502599853171771818959460675... . - Vaclav Kotesovec, Jan 17 2015

Extensions

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