A177524 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down.

1, 1, 2, 6, 24, 120, 715, 4970, 39480, 352800, 3502800, 38255900, 455795100, 5883052500, 81774966000, 1217871018000, 19346879737625, 326549862671250, 5835951345093750, 110091785625495000, 2186122850020215000, 45580964489553559375, 995625115672520581250

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..170

Formula

a(n) ~ c * d^n * n!, where d = 0.9928637443921790380857377558103269268777241137790934589694993..., c = 1.0369478195304845650491426260146999487076420703190374702807322... . - Vaclav Kotesovec, Aug 29 2014

Maple

b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
      add(b(u-j, o+j-1, `if`(t=1, 1, t+1)), j=1..u)+
      add(b(u+j-1, o-j, 2), 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 == 0, 1,
     Sum[b[u - j, o + j - 1, If[t == 1, 1, t + 1]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, 2], {j, 1, o}]]];
a[n_] := If[n == 0, 1, Sum[b[j - 1, n - j, 1], {j, 1, n}]];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 20 2022, after Alois P. Heinz *)

Crossrefs

Columns k=16,30 of A242784.

Sequence in context: A177531 A121987 A324132 * A223905 A164872 A226437

Adjacent sequences: A177521 A177522 A177523 * A177525 A177526 A177527

Keyword

nonn

Author

R. H. Hardin, May 10 2010

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 20 2013

Status

approved