A177526 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down.

1, 1, 2, 6, 24, 120, 680, 4480, 33600, 285434, 2684680, 27812170, 313926560, 3842611240, 50625902600, 714873188122, 10764733339179, 172258243070682, 2918333808555034, 52191694000877878, 982479378895814520, 19419959862935129834, 402131210857811703926

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 = 0.94123983763344712685016041467..., c = 1.3558011859159420827133973526... . - 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, 6][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 2][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, 6}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 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=18,22 of A242784.

Sequence in context: A152340 A152347 A228393 * A214611 A177528 A177527

Adjacent sequences: A177523 A177524 A177525 * A177527 A177528 A177529

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

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

Status

approved