A177535 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down, up.

1, 1, 2, 6, 24, 120, 720, 5011, 39856, 356616, 3545280, 38768400, 462487631, 5977005477, 83186290826, 1240460869290, 19730730733920, 333451122953921, 5966845400766578, 112703780178989573, 2240828272067529040, 46780834679854338540, 1023129822229674425971

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 = 0.9941229421721758523485136789468386588070503717223814960732680334748287519..., c = 1.036291721564809563490641628457988175489113294377683691938047314400726... . - 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, 4, 5, 6, 1][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 2, 2, 7][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 22 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, 4, 5, 6, 1}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 2, 2, 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

Column k=33 of A242784.

Sequence in context: A177537 A177541 A177551 * A263929 A324139 A324138

Adjacent sequences: A177532 A177533 A177534 * A177536 A177537 A177538

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

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

Status

approved