OFFSET
0,2
COMMENTS
Also the number of signed permutations of size n invariant under D and avoiding (-2, 1) and (2, -1).
LINKS
Andy Hardt and Justin M. Troyka, Restricted Symmetric Signed Permutations, 2012.
FORMULA
a(n) = 2*a(n-1) + n*a(n-2) - Sum_{j=1..k-3} j*a(j)*|S_{k-j-3}^D|, where S_n^D is the set of unsigned permutations of length n invariant under D.
a(n) = 2*a(n-1) + n*a(n-2) - Sum_{j=1..n-3} j*a(j)*A000085(n-j-2). - Andrew Howroyd, Dec 09 2018
MAPLE
inv := proc(n) option remember; if n<2 then 1 else inv(n-1)+(n-1)*inv(n-2) fi end:
a := proc(n) option remember; if n < 2 then n+1 else
2*a(n-1) + n*a(n-2) - add(j*a(j)*inv(n-j-2), j=1..n-3) fi end:
seq(a(n), n=0..26); # Peter Luschny, Dec 09 2018
MATHEMATICA
inv[n_] := inv[n] = If[n<2, 1, inv[n-1] + (n-1) inv[n-2]];
a[n_] := a[n] = If[n<2, n+1, 2 a[n-1] + n a[n-2] - Sum[j a[j] inv[n-j-2], {j, 1, n-3}]];
Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Jun 26 2019, after Peter Luschny *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Andy Hardt, Aug 04 2011
EXTENSIONS
Terms a(9) and beyond from Peter Luschny, Dec 09 2018
STATUS
approved