A264451 Number of permutations of [n] with exactly two (possibly overlapping) occurrences of the generalized pattern 12-3.

1, 13, 112, 843, 6089, 43887, 321357, 2411686, 18631631, 148490575, 1221894598, 10382648734, 91073271181, 824221683639, 7690752545310, 73932347642395, 731636916804531, 7447376286108705, 77913394499688645, 837113596053971008, 9229808681562243113

Offset

4,2

Links

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

Example

a(4) = 1: 1243.
a(5) = 13: 13254, 13524, 13542, 14235, 21354, 23154, 23514, 23541, 24135, 31254, 34125, 41253, 51243.

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, 3), polynom), j=1..o))
    end:
a:= n-> coeff(b(n, 0), x, 2):
seq(a(n), n=4..25);

Crossrefs

Column k=2 of A260665.

Sequence in context: A299050 A299812 A099111 * A299687 A300319 A199642

Adjacent sequences: A264448 A264449 A264450 * A264452 A264453 A264454

Keyword

nonn

Author

Alois P. Heinz, Nov 14 2015

Status

approved