|
|
A177525
|
|
Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up.
|
|
2
|
|
|
1, 1, 2, 6, 24, 120, 701, 4774, 37128, 324576, 3153961, 33709743, 393044544, 4964774568, 67536381485, 984328864872, 15302821821071, 252773481889854, 4420945845050347, 81616873102658977, 1586065426493434829, 32363206963164145993, 691807691094619216393
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ c * d^n * n!, where d = 0.971652908773770631708593889167049741726729704564696579529716779..., c = 1.15870633318154171410681190800508780736090448111042904596... . - 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, 5, 1][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 2, 2, 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, 5, 1}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 2, 2, 6}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|