A177549 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, down, up, up.

1, 1, 2, 6, 24, 120, 720, 4969, 39184, 347544, 3424320, 37150741, 439774085, 5639099103, 77873192126, 1152123776419, 18181366630226, 304851804959519, 5412206888619242, 101424438933572112, 2000731009697485843, 41440364401733715980, 899211137893661967405

Offset: 0

Author

R. H. Hardin, May 10 2010

Keywords

• nonn

Links

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

Crossrefs

Column k=51 of A242784.

Programs

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, 5, 1, 1][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 3, 3, 2, 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, 5, 1, 1}[[t]]], {j, 1, u}] + Sum[b[u+j-1, o-j, {2, 3, 3, 2, 6, 7}[[t]]], {j, 1, o}]]]; a[n_] := b[n, 0, 1]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Nov 11 2016, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n * n!, where d = 0.986314277283772995320277545416339641125925..., c = 1.08332315844132327949722334709840176297166... . - Vaclav Kotesovec, Jan 17 2015

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 23 2013