A177527 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up.

1, 1, 2, 6, 24, 120, 694, 4676, 35952, 310464, 2984176, 31536583, 363591384, 4541789148, 61089594448, 880428095803, 13534614549829, 221066397540186, 3823205871530350, 69792946997645295, 1341134146478847104, 27059669661295560098, 571973335506443017436

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..170

Formula

a(n) ~ c * d^n * n!, where d = 0.96079505301634594056671142147783512755736606..., c = 1.2266835832918378326758739778897107143678546... . - Vaclav Kotesovec, Jan 17 2015

Maple

b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
      add(b(u-j, o+j-1, [1, 3, 4, 1, 3][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 6][t]), j=1..o)))
    end:
a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 21 2013

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 3}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 6}[[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=19,25 of A242784.

Sequence in context: A177526 A214611 A177528 * A068200 A189847 A189284

Adjacent sequences: A177524 A177525 A177526 * A177528 A177529 A177530

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 21 2013

Status

approved