A229884 - OEIS

%I #20 Dec 21 2020 07:15:48

%S 1,1,1,1,1,4,10,20,125,461,1301,11210,55220,202840,2223859,13690951,

%T 61889101,823947856,6087160726,32676403052,511799407517,4411241879141,

%U 27418828825961,493869702112622,4864805677935368,34361404413755056,699648473127100771

%N Number of 3 up, 3 down permutations of [n].

%C Limit n->infinity (a(n)/n!)^(1/n) = 0.4494840644898... . - _Vaclav Kotesovec_, Sep 06 2014

%H Alois P. Heinz, <a href="/A229884/b229884.txt">Table of n, a(n) for n = 0..200</a>

%e a(4) = 1: 1234.

%e a(5) = 4: 12354, 12453, 13452, 23451.

%e a(6) = 10: 123654, 124653, 125643, 134652, 135642, 145632, 234651, 235641, 245631, 345621.

%e a(7) = 20: 1237654, 1247653, 1257643, 1267543, 1347652, 1357642, 1367542, 1457632, 1467532, 1567432, 2347651, 2357641, 2367541, 2457631, 2467531, 2567431, 3457621, 3467521, 3567421, 4567321.

%p b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(`if`(t=3,

%p        b(o-j, u+j-1, 1), b(u+j-1, o-j, t+1)), j=1..o))

%p     end:

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

%p seq(a(n), n=0..30);

%t b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Sum[If[t == 3, b[o - j, u + j - 1, 1], b[u + j - 1, o - j, t + 1]], {j, 1, o}]];

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

%t a /@ Range[0, 30] (* _Jean-François Alcover_, Dec 21 2020, after _Alois P. Heinz_ *)

%Y Column k=3 of A229892.

%Y Cf. A005982.

%K nonn,eigen

%O 0,6

%A _Alois P. Heinz_, Oct 02 2013