A177537 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up, up.

1, 1, 2, 6, 24, 120, 720, 4985, 39440, 351000, 3470400, 37738800, 447766925, 5755249449, 79663786022, 1181466923370, 18690124534560, 314145239141775, 5590784473674106, 105025821614503735, 2076805450110696320, 43120601826854807940, 937944680532722764045

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..175

Formula

a(n) ~ c * d^n * n!, where d = 0.9887118103491926984294539697508784179435508781692068887..., c = 1.071215254418408841713627749833237640463228021776737... . - 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, 1, 3][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 2, 6, 7][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 24 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, 1, 3}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 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=35,49 of A242784.

Sequence in context: A177536 A177549 A177542 * A177541 A177551 A177535

Adjacent sequences: A177534 A177535 A177536 * A177538 A177539 A177540

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 24 2013

Status

approved