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

15, 576, 13572, 259968, 4532034, 75929856, 1259571660, 21052915200, 358291184565, 6248298977280, 112089186363960, 2073140406374400, 39582481045276260, 780630651563728896, 15904712294529556680, 334724021030855393280, 7274246960518735730715

Offset: 7

Author

Alois P. Heinz, Oct 28 2015

Keywords

• nonn

Examples

			a(7) = 15: 1325476, 1326475, 1327465, 1425376, 1426375, 1427365, 1524376, 1526374, 1527364, 1624375, 1625374, 1627354, 1724365, 1725364, 1726354.
a(8) = 576: 12436587, 12437586, 12438576, ..., 81724365, 81725364, 81726354.
a(9) = 13572: 123547698, 123548697, 123549687, ..., 981724365, 981725364, 981726354.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..200

Crossrefs

Column k=3 of A197365.

Programs

Maple

b:= proc(u, o, t) option remember; series(`if`(u+o=0, 1,
      add(b(u-j, o+j-1, 0)*`if`(j<=t, x, 1), j=1..u)+
      add(b(u+j-1, o-j, j-1), j=1..o)), x, 4)
    end:
a:= n-> coeff(b(n, 0$2), x, 3):
seq(a(n), n=7..30);

Formula

a(n) = A197365(n,3).