login
A227883
Number of permutations of [n] with exactly one occurrence of the consecutive step pattern up, down, up.
4
0, 0, 0, 0, 5, 50, 328, 2154, 16751, 144840, 1314149, 12735722, 134159743, 1519210786, 18272249418, 233231701166, 3159471128588, 45243728569842, 682183513506619, 10807962134238068, 179606706777512992, 3123700853586733882, 56737351453843424893
OFFSET
0,5
LINKS
Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..460 (first 195 terms from Alois P. Heinz)
FORMULA
a(n) ~ c * d^n * n! * n, where d = A245758 = 0.782704180171521701844707..., c = 0.575076701401064911213333442496869737011... . - Vaclav Kotesovec, Aug 22 2014
EXAMPLE
a(4) = 5: 1324, 1423, 2314, 2413, 3412.
a(5) = 50: 12435, 12534, 13245, ..., 52314, 52413, 53412.
MAPLE
b:= proc(u, o, t) option remember;
`if`(t=7, 0, `if`(u+o=0, `if`(t in [4, 5, 6], 1, 0),
add(b(u-j, o+j-1, [1, 3, 1, 5, 6, 6][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 4, 4, 7, 4][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);
MATHEMATICA
b[u_, o_, t_] := b[u, o, t] =
If[t == 7, 0, If[u + o == 0, If[4 <= t <= 6, 1, 0],
Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 6, 6}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 4, 4, 7, 4}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *)
CROSSREFS
Column k=1 of A227884.
Sequence in context: A064054 A301821 A301997 * A227261 A036291 A060347
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 25 2013
STATUS
approved