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A177543
Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up, down.
2
1, 1, 2, 6, 24, 120, 720, 4768, 35968, 312064, 3004160, 31764480, 365798400, 4555499520, 61232590848, 882227765248, 13547017240576, 221038858829824, 3818608204709888, 69637156745773056, 1336921845773107200, 26947721453843251200, 569023211226594803712
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * d^n * n!, where d = 0.9598365530271216889440240044515..., c = 1.2474579024498809739499621681... . - 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, 5, 1, 7][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 4, 2, 6, 2][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25); # Alois P. Heinz, Oct 24 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, 5, 1, 7}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6, 2}[[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
Column k=42 of A242784.
Sequence in context: A152363 A152359 A152362 * A189842 A189271 A152366
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 10 2010
EXTENSIONS
a(17)-a(22) from Alois P. Heinz, Oct 24 2013
STATUS
approved