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A177545
Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, down, down.
2
1, 1, 2, 6, 24, 120, 720, 4929, 38544, 338904, 3309120, 35521200, 415704960, 5271197205, 71977504692, 1053008012790, 16431803844480, 272435676775200, 4782657847248000, 88624515772410633, 1728678866577622920, 35404942557640528620, 759655818204633900000
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * d^n * n!, where d = 0.9752820884477652193970997660966130503977714987577677..., c = 1.1721546677937404500752065441275892023818795500231... . - 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, 3, 1, 3, 6, 7][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 4, 5, 2, 4][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25); # Alois P. Heinz, Oct 22 2013
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, 3, 1, 3, 6, 7}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 2, 4}[[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=44,50 of A242784.
Sequence in context: A068201 A189848 A189285 * A177538 A177550 A177536
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 10 2010
EXTENSIONS
a(17)-a(22) from Alois P. Heinz, Oct 22 2013
STATUS
approved