A177539 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down, up.

1, 1, 2, 6, 24, 120, 720, 4859, 37424, 323784, 3107520, 32749200, 376929246, 4698101279, 63058148792, 906829731450, 13911580276800, 226738605155619, 3912973221007668, 71280397766349665, 1366816300552776920, 27519285653572655340, 580456044040809459821

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 = 0.958757960478580745672487123002941621817..., c = 1.30438280919882137519668832091857761... . - 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, 4][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 2, 7][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, 6, 4}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 2, 7}[[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=37,41 of A242784.

Sequence in context: A147739 A147738 A147737 * A177546 A177544 A177540

Adjacent sequences: A177536 A177537 A177538 * A177540 A177541 A177542

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

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

Status

approved