A227883 Number of permutations of [n] with exactly one occurrence of the consecutive step pattern up, down, up.

0, 0, 0, 0, 5, 50, 328, 2154, 16751, 144840, 1314149, 12735722, 134159743, 1519210786, 18272249418, 233231701166, 3159471128588, 45243728569842, 682183513506619, 10807962134238068, 179606706777512992, 3123700853586733882, 56737351453843424893

Offset

0,5

Links

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..460 (first 195 terms from Alois P. Heinz)

Formula

a(n) ~ c * d^n * n! * n, where d = A245758 = 0.782704180171521701844707..., c = 0.575076701401064911213333442496869737011... . - Vaclav Kotesovec, Aug 22 2014

Example

a(4) = 5: 1324, 1423, 2314, 2413, 3412.
a(5) = 50: 12435, 12534, 13245, ..., 52314, 52413, 53412.

Maple

b:= proc(u, o, t) option remember;
      `if`(t=7, 0, `if`(u+o=0, `if`(t in [4, 5, 6], 1, 0),
      add(b(u-j, o+j-1, [1, 3, 1, 5, 6, 6][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 4, 7, 4][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);

Mathematica

b[u_, o_, t_] := b[u, o, t] =
    If[t == 7, 0, If[u + o == 0, If[4 <= t <= 6, 1, 0],
    Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 6, 6}[[t]]], {j, 1, u}] +
    Sum[b[u + j - 1, o - j, {2, 2, 4, 4, 7, 4}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *)

Crossrefs

Column k=1 of A227884.

Cf. A177477, A245758.

Sequence in context: A064054 A301821 A301997 * A227261 A036291 A060347

Adjacent sequences: A227880 A227881 A227882 * A227884 A227885 A227886

Keyword

nonn

Author

Alois P. Heinz, Oct 25 2013

Status

approved