A177551 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, up, up, up.

1, 1, 2, 6, 24, 120, 720, 5006, 39776, 355536, 3530880, 38581456, 459905790, 5938902464, 82590382604, 1230586598456, 19557934834104, 330265974019619, 5905113439990368, 111448391640387360, 2214092715361273978, 46185648021443324656, 1009303225985497077402

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Formula

a(n) ~ c * d^n * n!, where d = 0.993326320961568877764783962159580548643374705129260577..., c = 1.0404765828695886736964990440705643676428197038942922... . - 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, 1, 4][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 3, 3, 5, 6, 7][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 23 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, 1, 4}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 3, 3, 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=55,59 of A242784.

Sequence in context: A177542 A177537 A177541 * A177535 A263929 A324139

Adjacent sequences: A177548 A177549 A177550 * A177552 A177553 A177554

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Status

approved