|
|
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)):
|
|
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];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|