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A193777 Number of signed permutations of size 2n invariant under D and D'bar and avoiding (-2, 1) and (2, -1). 3
1, 2, 6, 18, 58, 190, 642, 2206, 7746, 27662, 100738, 373550, 1413506, 5457710, 21546466, 87025806, 360264258, 1529624366, 6669850466, 29877013902, 137560725890, 650780790894, 3162711095074, 15774862353614, 80687636530882, 422713072650286, 2265833731786594 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the number of signed permutations of size n invariant under D and avoiding (-2, 1) and (2, -1).

LINKS

Table of n, a(n) for n=0..26.

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-Fran├žois Alcover, Jun 26 2019, after Peter Luschny *)

CROSSREFS

Cf. A193778, A000085.

Sequence in context: A081057 A000137 A151282 * A157004 A293067 A085139

Adjacent sequences:  A193774 A193775 A193776 * A193778 A193779 A193780

KEYWORD

nonn

AUTHOR

Andy Hardt, Aug 04 2011

EXTENSIONS

Terms a(9) and beyond from Peter Luschny, Dec 09 2018

STATUS

approved

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Last modified August 11 00:32 EDT 2020. Contains 336403 sequences. (Running on oeis4.)