A177525 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up.

1, 1, 2, 6, 24, 120, 701, 4774, 37128, 324576, 3153961, 33709743, 393044544, 4964774568, 67536381485, 984328864872, 15302821821071, 252773481889854, 4420945845050347, 81616873102658977, 1586065426493434829, 32363206963164145993, 691807691094619216393

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 = 0.971652908773770631708593889167049741726729704564696579529716779..., c = 1.15870633318154171410681190800508780736090448111042904596... . - 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, 5, 1][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 2, 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, 5, 1}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 2, 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

Column k=17 of A242784.

Sequence in context: A189847 A189284 A274970 * A177532 A242573 A223034

Adjacent sequences: A177522 A177523 A177524 * A177526 A177527 A177528

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

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

Status

approved