A177530 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, up.

1, 1, 2, 6, 24, 120, 706, 4844, 37968, 334656, 3278896, 35330098, 415289184, 5288377848, 72522052240, 1065579141202, 16700472769061, 278099720959114, 4903387952699182, 91258390273541562, 1787828412527348984, 36776310494510881628, 792526608079806841508

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) ~ c * d^n * n!, where d = 0.9795419074893388679910049642242424087370823270695747551625158..., c = 1.111068410182136129001099552719852410280865324840041630689... . - Vaclav Kotesovec, Jan 17 2015

Maple

b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 1, 3, 3][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 5, 6][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 21 2013

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 1, 3, 3}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 6}[[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=23,29 of A242784.

Sequence in context: A177532 A242573 A223034 * A324134 A324135 A177531

Adjacent sequences: A177527 A177528 A177529 * A177531 A177532 A177533

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 21 2013

Status

approved