A193776 Number of signed permutations of length n invariant under the reverse complement and avoiding (-2, -1), (-2, 1), (2, -1).

1, 2, 3, 5, 12, 17, 65, 80, 473, 527, 4444, 4679, 51391, 52628, 703659, 711449, 11098896, 11156477, 197809793, 198299024, 3927270089, 3931960343, 85908742132, 85958728847, 2052375195679, 2052960568556, 53160174898371, 53167638586121, 1483752628890840, 1483855482962885, 44391655829672177

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Formula

a(2k) = 2^k k! + \sum_{j=0}^{k-1}(k-j-1)! a(2j)

a(2k+1) = (2^k + 1)k! + \sum_{j=0}^{k-1}(k-j-1)! a(2j+1)

Example

For n = 2, the permutations are (1, 2), (2, 1), (-1, -2), (-2, -1).

Mathematica

a[n_] := a[n] = If[EvenQ[n],
   Sum[a[2j]*(n/2 - j - 1)!, {j, 0, n/2 - 1}] + 2^(n/2)*(n/2)!,
   Sum[a[2j+1]*((1/2)*(n - 2j - 3))!, {j, 0, (n - 3)/2}] +
      (2^((n - 1)/2) + 1)*((n - 1)/2)!];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Apr 10 2024 *)

Crossrefs

Sequence in context: A002139 A140489 A331101 * A051915 A064688 A089891

Adjacent sequences: A193773 A193774 A193775 * A193777 A193778 A193779

Keyword

nonn

Author

Andy Hardt, Aug 04 2011

Status

approved