A227883 - OEIS

%I #19 Dec 20 2020 07:32:00

%S 0,0,0,0,5,50,328,2154,16751,144840,1314149,12735722,134159743,

%T 1519210786,18272249418,233231701166,3159471128588,45243728569842,

%U 682183513506619,10807962134238068,179606706777512992,3123700853586733882,56737351453843424893

%N Number of permutations of [n] with exactly one occurrence of the consecutive step pattern up, down, up.

%H Alois P. Heinz and Vaclav Kotesovec, <a href="/A227883/b227883.txt">Table of n, a(n) for n = 0..460</a> (first 195 terms from Alois P. Heinz)

%F a(n) ~ c * d^n * n! * n, where d = A245758 = 0.782704180171521701844707..., c = 0.575076701401064911213333442496869737011... . - _Vaclav Kotesovec_, Aug 22 2014

%e a(4) = 5: 1324, 1423, 2314, 2413, 3412.

%e a(5) = 50: 12435, 12534, 13245, ..., 52314, 52413, 53412.

%p b:= proc(u, o, t) option remember;

%p       `if`(t=7, 0, `if`(u+o=0, `if`(t in [4, 5, 6], 1, 0),

%p       add(b(u-j, o+j-1, [1, 3, 1, 5, 6, 6][t]), j=1..u)+

%p       add(b(u+j-1, o-j, [2, 2, 4, 4, 7, 4][t]), j=1..o)))

%p     end:

%p a:= n-> b(n, 0, 1):

%p seq(a(n), n=0..25);

%t b[u_, o_, t_] := b[u, o, t] =

%t     If[t == 7, 0, If[u + o == 0, If[4 <= t <= 6, 1, 0],

%t     Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 6, 6}[[t]]], {j, 1, u}] +

%t     Sum[b[u + j - 1, o - j, {2, 2, 4, 4, 7, 4}[[t]]], {j, 1, o}]]];

%t a[n_] := b[n, 0, 1];

%t a /@ Range[0, 25] (* _Jean-François Alcover_, Dec 20 2020, after _Alois P. Heinz_ *)

%Y Column k=1 of A227884.

%Y Cf. A177477, A245758.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Oct 25 2013