A264452 Number of permutations of [n] with exactly three (possibly overlapping) occurrences of the generalized pattern 12-3.

1, 12, 103, 811, 6273, 48806, 386041, 3122069, 25900188, 220791812, 1935811756, 17461471292, 162038542377, 1546528485770, 15174625184321, 152994813139537, 1584120732683571, 16834244135840106, 183496533502593453, 2050337555698723711, 23470542944212951050

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..500

Example

a(4) = 1: 1234.
a(5) = 12: 12534, 12543, 13245, 13425, 13452, 21345, 23145, 23415, 23451, 31245, 41235, 51234.

Maple

b:= proc(u, o) option remember; `if`(u+o=0, 1, add(
       b(u-j, o+j-1), j=1..u)+add(convert(series(
       b(u+j-1, o-j)*x^(o-j), x, 4), polynom), j=1..o))
    end:
a:= n-> coeff(b(n, 0), x, 3):
seq(a(n), n=4..25);

Crossrefs

Column k=3 of A260665.

Sequence in context: A005771 A016228 A016276 * A078397 A228988 A266959

Adjacent sequences: A264449 A264450 A264451 * A264453 A264454 A264455

Keyword

nonn

Author

Alois P. Heinz, Nov 14 2015

Status

approved