A228422 Number of permutations of [n] with exactly two (possibly overlapping) occurrences of some of the consecutive patterns 123, 1432, 2431, 3421.

0, 0, 0, 0, 1, 14, 164, 1589, 15034, 139465, 1334945, 13108425, 134906641, 1443572465, 16238742806, 190546010823, 2347715040542, 30162115442344, 405859441345002, 5684963539755583, 83163913991455832, 1263763900212930657, 20000260465018111763

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..185

Formula

a(n) ~ c * (2/Pi)^n * n! * n^2, where c = 1.286210080518397686... . - Vaclav Kotesovec, Aug 28 2014

Example

a(4) = 1: 1234.
a(5) = 14: 12354, 12453, 12543, 13452, 13542, 14532, 21345, 23451, 23541, 24531, 31245, 34521, 41235, 51234.

Maple

b:= proc(u, o, t, c) option remember;
      `if`(c<0, 0, `if`(u+o=0, `if`(c=0, 1, 0),
      add(b(u+j-1, o-j, [2, 2, 2][t], `if`(t=2, c-1, c)), j=1..o)+
      add(b(u-j, o+j-1, [1, 3, 1][t], `if`(t=3, c-1, c)), j=1..u)))
    end:
a:= n-> b(n, 0, 1, 2):
seq(a(n), n=0..25);

Mathematica

b[u_, o_, t_, c_] := b[u, o, t, c] =
    If[c<0, 0, If[u+o == 0, If[c == 0, 1, 0],
    Sum[b[u+j-1, o-j, 2,              If[t == 2, c-1, c]], {j, 1, o}] +
    Sum[b[u-j, o+j-1, {1, 3, 1}[[t]], If[t == 3, c-1, c]], {j, 1, u}]]];
a[n_] := b[n, 0, 1, 2];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *)

Crossrefs

Column k=2 of A231210.

Sequence in context: A153664 A016146 A269539 * A218089 A273587 A125449

Adjacent sequences: A228419 A228420 A228421 * A228423 A228424 A228425

Keyword

nonn

Author

Alois P. Heinz, Nov 09 2013

Status

approved