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A263888 Number of permutations of [n] containing exactly four occurrences of the consecutive pattern 132.

%I A263888 #6 Oct 30 2015 21:56:21
%S A263888 105,7968,306729,8862336,221041785,5090751360,112456455285,
%T A263888 2438635714560,52685573396310,1145097655557120,25201633254603750,
%U A263888 564111809386352640,12881077471698335550,300654388617807974400,7182803417002318476630,175794354355113443819520
%N A263888 Number of permutations of [n] containing exactly four occurrences of the consecutive pattern 132.
%H A263888 Alois P. Heinz, <a href="/A263888/b263888.txt">Table of n, a(n) for n = 9..100</a>
%F A263888 a(n) = A197365(n,4).
%e A263888 a(9) = 105: 132547698, 132548697, 132549687, ..., 192835476, 192836475, 192837465.
%p A263888 b:= proc(u, o, t) option remember; series(`if`(u+o=0, 1,
%p A263888       add(b(u-j, o+j-1, 0)*`if`(j<=t, x, 1), j=1..u)+
%p A263888       add(b(u+j-1, o-j, j-1), j=1..o)), x, 5)
%p A263888     end:
%p A263888 a:= n-> coeff(b(n, 0$2), x, 4):
%p A263888 seq(a(n), n=9..35);
%Y A263888 Column k=4 of A197365.
%K A263888 nonn
%O A263888 9,1
%A A263888 _Alois P. Heinz_, Oct 28 2015