A264461 Number of permutations of [n] with exactly two (possibly overlapping) occurrences of the generalized pattern 23-1.

3, 23, 152, 984, 6460, 43626, 304939, 2211467, 16649780, 130097338, 1054226016, 8850736900, 76901730751, 690749091147, 6406953787268, 61300205459232, 604367205789092, 6133919028981542, 64027105979768111, 686736004045762143, 7562191796264603160

Offset: 4

Author

Alois P. Heinz, Nov 14 2015

Keywords

• nonn

Examples

			a(4) = 3: 2341, 3412, 3421.
a(5) = 23: 13452, 14523, 14532, 23415, 23514, 23541, 24351, 25341, 32451, 34125, 34152, 34215, 35124, 35142, 35214, 35412, 35421, 42351, 43512, 43521, 52341, 53412, 53421.
		

Links

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

Crossrefs

Column k=2 of A260670.

Programs

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

Mathematica

b[u_, o_] := b[u, o] = If[u+o == 0, 1, Sum[b[u-j, o+j-1], {j, 1, u}] + Sum[Series[b[u+j-1, o-j] x^u, {x, 0, 3}] // Normal, {j, 1, o}]];
a[n_] := Coefficient[b[n, 0], x, 2];
a /@ Range[4, 25] (* Jean-François Alcover, Sep 28 2020, after Maple *)