A177550 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, up, down, down.

1, 1, 2, 6, 24, 120, 720, 4950, 38880, 343440, 3369600, 36352800, 427680000, 5452027218, 74846801304, 1100895311340, 17272089457920, 287920937620800, 5081935953473280, 94681381716805374, 1856848184953043760, 38236452673395920040, 824863858830361247040

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) ~ c * d^n * n!, where d = 0.98057763883233672986361278986560196505968263650602..., c = 1.129827226571293707156672292645277720979050046894688... . - Vaclav Kotesovec, Jan 17 2015

Maple

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
      add(b(u-j, o+j-1, [1, 1, 4, 1, 6, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 3, 3, 5, 3, 2][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 29 2013

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 1, 4, 1, 6, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 3, 3, 5, 3, 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

Column k=52 of A242784.

Sequence in context: A189285 A177545 A177538 * A177536 A177549 A177542

Adjacent sequences: A177547 A177548 A177549 * A177551 A177552 A177553

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 29 2013

Status

approved