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A177527 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up. 2
1, 1, 2, 6, 24, 120, 694, 4676, 35952, 310464, 2984176, 31536583, 363591384, 4541789148, 61089594448, 880428095803, 13534614549829, 221066397540186, 3823205871530350, 69792946997645295, 1341134146478847104, 27059669661295560098, 571973335506443017436 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * d^n * n!, where d = 0.96079505301634594056671142147783512755736606..., c = 1.2266835832918378326758739778897107143678546... . - Vaclav Kotesovec, Jan 17 2015
MAPLE
b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
add(b(u-j, o+j-1, [1, 3, 4, 1, 3][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 2, 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, 4, 1, 3}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 2, 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=19,25 of A242784.
Sequence in context: A177526 A214611 A177528 * A068200 A189847 A189284
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 10 2010
EXTENSIONS
a(17)-a(22) from Alois P. Heinz, Oct 21 2013
STATUS
approved

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Last modified June 8 00:04 EDT 2023. Contains 363157 sequences. (Running on oeis4.)