A263888 - OEIS

%I #6 Oct 30 2015 21:56:21

%S 105,7968,306729,8862336,221041785,5090751360,112456455285,

%T 2438635714560,52685573396310,1145097655557120,25201633254603750,

%U 564111809386352640,12881077471698335550,300654388617807974400,7182803417002318476630,175794354355113443819520

%N Number of permutations of [n] containing exactly four occurrences of the consecutive pattern 132.

%H Alois P. Heinz, <a href="/A263888/b263888.txt">Table of n, a(n) for n = 9..100</a>

%F a(n) = A197365(n,4).

%e a(9) = 105: 132547698, 132548697, 132549687, ..., 192835476, 192836475, 192837465.

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

%p       add(b(u-j, o+j-1, 0)*`if`(j<=t, x, 1), j=1..u)+

%p       add(b(u+j-1, o-j, j-1), j=1..o)), x, 5)

%p     end:

%p a:= n-> coeff(b(n, 0$2), x, 4):

%p seq(a(n), n=9..35);

%Y Column k=4 of A197365.

%K nonn

%O 9,1

%A _Alois P. Heinz_, Oct 28 2015