|
|
A177528
|
|
Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, down.
|
|
3
|
|
|
1, 1, 2, 6, 24, 120, 685, 4550, 34440, 292320, 2746800, 28402925, 320224500, 3909695400, 51396618000, 723952593000, 10876269801125, 173607227828250, 2934111079914750, 52343975053683000, 982945842995115000, 19381240178451775625, 400347201716808478750
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ c * d^n * n!, where d = 0.93892752514028508419326638408810575968441290684141..., c = 1.4248368339815259677105814450156343177071690245... . - 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, 5, 6][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 4, 2, 4][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, 1, 5, 6}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 4}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|