A177541 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, up.

1, 1, 2, 6, 24, 120, 720, 4990, 39520, 352080, 3484800, 37936800, 450606300, 5797965980, 80341280840, 1192794269400, 18889568419200, 317838157969125, 5662578565559400, 106488682710940108, 2107992477960872320, 43815112964794432080, 954074378001971825930

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..150

Formula

a(n) ~ c * d^n * n!, where d = 0.98977300089321592191180343193285102663621683..., c = 1.06422234334396404091033045795479059186356... . - Vaclav Kotesovec, Jan 17 2015

Maple

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o=0, 1,
      add(b(u-j, o+j-1, [1, 3, 4, 1, 3, 3][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 6, 7][t]), j=1..o)))
    end:
a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 20 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, 1, 3, 3}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 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=39,57 of A242784.

Sequence in context: A177549 A177542 A177537 * A177551 A177535 A263929

Adjacent sequences: A177538 A177539 A177540 * A177542 A177543 A177544

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 20 2013

Status

approved