|
|
A177548
|
|
Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, down, down, down.
|
|
2
|
|
|
1, 1, 2, 6, 24, 120, 720, 5025, 40080, 359640, 3585600, 39322800, 470448000, 6097392939, 85106238492, 1272746220570, 20302567148160, 344103461618400, 6175195781293440, 116975122363277289, 2332451810975205960, 48833870901559002540, 1071107370496773577440
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ c * d^n * n!, where d = 0.99698626702423025316812958090212389097043667361318991688710688185165..., c = 1.018367520648807878150063272123153629935889863110044893080319840979... . - Vaclav Kotesovec, Jan 17 2015
|
|
MAPLE
|
b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
add(b(u-j, o+j-1, [1, 1, 4, 5, 6, 7][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 3, 3, 2, 2, 2][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
|
|
MATHEMATICA
|
b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
Sum[b[u - j, o + j - 1, {1, 1, 4, 5, 6, 7}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 3, 3, 2, 2, 2}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|