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A263887 Number of permutations of [n] containing exactly three occurrences of the consecutive pattern 132.

%I A263887 #6 Oct 29 2015 18:19:43
%S A263887 15,576,13572,259968,4532034,75929856,1259571660,21052915200,
%T A263887 358291184565,6248298977280,112089186363960,2073140406374400,
%U A263887 39582481045276260,780630651563728896,15904712294529556680,334724021030855393280,7274246960518735730715
%N A263887 Number of permutations of [n] containing exactly three occurrences of the consecutive pattern 132.
%H A263887 Alois P. Heinz, <a href="/A263887/b263887.txt">Table of n, a(n) for n = 7..200</a>
%F A263887 a(n) = A197365(n,3).
%e A263887 a(7) = 15: 1325476, 1326475, 1327465, 1425376, 1426375, 1427365, 1524376, 1526374, 1527364, 1624375, 1625374, 1627354, 1724365, 1725364, 1726354.
%e A263887 a(8) = 576: 12436587, 12437586, 12438576, ..., 81724365, 81725364, 81726354.
%e A263887 a(9) = 13572: 123547698, 123548697, 123549687, ..., 981724365, 981725364, 981726354.
%p A263887 b:= proc(u, o, t) option remember; series(`if`(u+o=0, 1,
%p A263887       add(b(u-j, o+j-1, 0)*`if`(j<=t, x, 1), j=1..u)+
%p A263887       add(b(u+j-1, o-j, j-1), j=1..o)), x, 4)
%p A263887     end:
%p A263887 a:= n-> coeff(b(n, 0$2), x, 3):
%p A263887 seq(a(n), n=7..30);
%Y A263887 Column k=3 of A197365.
%K A263887 nonn
%O A263887 7,1
%A A263887 _Alois P. Heinz_, Oct 28 2015