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

0,3

Links

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

Formula

a(n) ~ c * d^n * n!, where d = 0.986314277283772995320277545416339641125925..., c = 1.08332315844132327949722334709840176297166... . - 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, 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 *)

Crossrefs

Column k=51 of A242784.

Sequence in context: A177538 A177550 A177536 * A177542 A177537 A177541

Adjacent sequences: A177546 A177547 A177548 * A177550 A177551 A177552

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

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

Status

approved