A177544 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up, up.

1, 1, 2, 6, 24, 120, 720, 4885, 37840, 329400, 3182400, 33778800, 391590750, 4915323791, 66442003448, 962278914330, 14866633343040, 244014015391725, 4240899164064012, 77799960323395327, 1502369690026049320, 30462229695574890900, 647071778569768101485

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 = 0.96553264441829855042601163560012935129948..., c = 1.245410138868090155003662557978590938375... . - 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, 3, 1, 5, 1, 5][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 2, 6, 7][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 30 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, 3, 1, 5, 1, 5}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6, 7}[[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=43,53 of A242784.

Sequence in context: A147737 A177539 A177546 * A177540 A068201 A189848

Adjacent sequences: A177541 A177542 A177543 * A177545 A177546 A177547

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 30 2013

Status

approved