A230832 Number of permutations of [n] with exactly one occurrence of the consecutive step pattern up, down, up, down.

0, 0, 0, 0, 0, 16, 192, 1472, 12800, 132352, 1366016, 14781952, 178102272, 2282645504, 30639611904, 440041603072, 6720063012864, 107722700685312, 1818098902499328, 32319047553515520, 601556224722337792, 11702621573275975680, 237913839294912397312

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..460

Formula

a(n) ~ c * d^n * n! * n, where d = 0.87361286073825385348141673848..., c = 0.2252746... . - Vaclav Kotesovec, Aug 28 2014

Example

a(5) = 16: 13254, 14253, 14352, 15243, 15342, 23154, 24153, 24351, 25143, 25341, 34152, 34251, 35142, 35241, 45132, 45231.
a(6) = 192: 124365, 125364, 125463, ..., 635241, 645132, 645231.
a(7) = 1472: 1235476, 1236475, 1236574, ..., 7635241, 7645132, 7645231.

Maple

b:= proc(u, o, t) option remember; `if`(t=9, 0,
      `if`(u+o=0, `if`(t>4, 1, 0),
      add(b(u-j, o+j-1, [1, 3, 1, 5, 7, 9, 7, 5][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 2, 6, 8, 8, 8][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 == 9, 0,
    If[u + o == 0, If[t > 4, 1,   0],
    Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 7, 9, 7, 5}[[t]]], {j, 1, u}] +
    Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6, 8, 8, 8}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
a /@ Range[0, 25] (* after Alois P. Heinz *)

Crossrefs

Column k=1 of A230797.

Sequence in context: A302298 A305773 A317122 * A305590 A232426 A317008

Adjacent sequences: A230829 A230830 A230831 * A230833 A230834 A230835

Keyword

nonn

Author

Alois P. Heinz, Oct 30 2013

Status

approved