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Number of 6 up, 6 down permutations of [n].
2

%I #11 Oct 04 2013 07:04:50

%S 1,1,1,1,1,1,1,1,7,28,84,210,462,924,11220,74283,354563,1363571,

%T 4482323,13058891,226630385,2101302530,13794660782,71790720848,

%U 314709809876,1206605493016,27221495651416,324504194839891,2711270620975411,17790823624994551

%N Number of 6 up, 6 down permutations of [n].

%H Alois P. Heinz, <a href="/A229887/b229887.txt">Table of n, a(n) for n = 0..200</a>

%e a(7) = 1: 1234567.

%e a(8) = 7: 12345687, 12345786, 12346785, 12356784, 12456783, 13456782, 23456781.

%e a(9) = 28: 123456987, 123457986, ..., 245678931, 345678921.

%p b:= proc(u, o, t) option remember; `if`(u+o=0, 1, add(`if`(t=6,

%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..35);

%Y Column k=6 of A229892.

%K nonn,eigen

%O 0,9

%A _Alois P. Heinz_, Oct 02 2013