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

0,3

Links

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

Formula

a(n) ~ c * d^n * n!, where d = 0.98162590771907099517875504406285427992737137228..., c = 1.1133866874983726502599853171771818959460675... . - 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, 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 *)

Crossrefs

Columns k=36,54 of A242784.

Sequence in context: A189848 A189285 A177545 * A177550 A177536 A177549

Adjacent sequences: A177535 A177536 A177537 * A177539 A177540 A177541

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

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

Status

approved