OFFSET
0,6
COMMENTS
The counted patterns are: 1243, 1342, 2341 (=UUD), 1324, 1423, 2314, 2413, 3412 (=UDU), 2134, 3124, 4123 (=DUU).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..185
EXAMPLE
a(5) = 29: 12435, 12534, 13245, 13425, 13524, 14235, 14523, 15234, 21354, 21453, 23145, 23415, 23514, 24135, 24513, 25134, 31254, 31452, 32451, 34125, 34512, 35124, 41253, 41352, 42351, 45123, 51243, 51342, 52341.
a(6) = 230: 123546, 123645, 124365, ..., 651243, 651342, 652341.
a(7) = 1537: 1234657, 1234756, 1235476, ..., 7651243, 7651342, 7652341.
MAPLE
b:= proc(u, o, t, c) option remember;
`if`(c<0, 0, `if`(u+o=0, `if`(c=0, 1, 0),
add(b(u+j-1, o-j, [2, 3, 3, 6, 6, 3][t],
`if`(t in [5, 6], c-1, c)), j=1..o)+
add(b(u-j, o+j-1, [4, 5, 5, 4, 4, 5][t],
`if`(t=3, c-1, c)), j=1..u)))
end:
a:= n-> add(b(j-1, n-j, 1, 2), j=1..n):
seq(a(n), n=0..25);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 09 2013
STATUS
approved