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Number of permutations of [n] with exactly six (possibly overlapping) occurrences of the generalized pattern 12-3.
2

%I #6 Nov 14 2015 08:24:12

%S 1,17,238,2956,33343,355182,3681762,37839385,389940538,4056942189,

%T 42796503464,458995025669,5013561835833,55832699192796,

%U 634322118799677,7354538207075076,87032355679553323,1051183375285792257,12956782873283747998,162950022525866642259

%N Number of permutations of [n] with exactly six (possibly overlapping) occurrences of the generalized pattern 12-3.

%H Alois P. Heinz, <a href="/A264455/b264455.txt">Table of n, a(n) for n = 5..500</a>

%e a(5) = 1: 12345.

%e a(6) = 17: 124365, 124635, 124653, 125346, 132456, 134256, 134526, 134562, 213456, 231456, 234156, 234516, 234561, 312456, 412356, 512346, 612345.

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

%p b(u-j, o+j-1), j=1..u)+add(convert(series(

%p b(u+j-1, o-j)*x^(o-j), x, 7), polynom), j=1..o))

%p end:

%p a:= n-> coeff(b(n, 0), x, 6):

%p seq(a(n), n=5..25);

%Y Column k=6 of A260665.

%K nonn

%O 5,2

%A _Alois P. Heinz_, Nov 14 2015