A177534 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down, down.

1, 1, 2, 6, 24, 120, 720, 5034, 40224, 361584, 3611520, 39679200, 475580160, 6175139244, 86348433264, 1293675609960, 20674025187840, 351037594569600, 6311110770685440, 119767524064039062, 2392482308124881520, 50181968955048369480, 1102681392427432825920

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 = 0.99880260814201465936657157017137377717606254472452619578417647021809..., c = 1.0072348951217738673562195411256011395302888145883911883919110478... . - 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, `if`(t=1, 1, t+1)), j=1..u)+
      add(b(u+j-1, o-j, 2), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 21 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, If[t == 1, 1, t + 1]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, 2], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 20 2022, after Alois P. Heinz *)

Crossrefs

Columns k=32,62 of A242784.

Sequence in context: A324136 A177548 A193935 * A164873 A226438 A248839

Adjacent sequences: A177531 A177532 A177533 * A177535 A177536 A177537

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

a(18)-a(22) from Alois P. Heinz, Oct 21 2013

Status

approved