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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
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)):
seq(a(n), n=0..25); # Alois P. Heinz, Oct 21 2013
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];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)
CROSSREFS
Columns k=20,26 of A242784.
Cf. A317639.
Sequence in context: A228393 A177526 A214611 * A177527 A068200 A189847
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 10 2010
EXTENSIONS
a(17)-a(22) from Alois P. Heinz, Oct 21 2013
STATUS
approved