A193763 Number of signed permutations of length n avoiding (-2, 1) and (2, -1).

1, 2, 6, 22, 94, 462, 2606, 16862, 124782, 1048990, 9921550, 104447550, 1211190638, 15329157278, 210093682254, 3097760346238, 48869022535726, 821007386273118, 14630266558195214, 275575669958063678, 5469996402416702958, 114107289124208861470

Offset

0,2

Comments

Also the number of signed permutations of length 2*n invariant under Dbar and avoiding (-1, 2) and (1, -2).

Also the number of signed permutations of length 2*n invariant under R180bar and avoiding (-1, 2) and (1, -2).

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1, and for n > 0, a(n) = n! + Sum_{j=0..n-1} (n-j)! * a(j).

a(n) is the sum of top row terms of M^n, M = an infinite square production matrix as follows:

1, 1, 0, 0, 0, 0,...

2, 0, 2, 0, 0, 0,...

3, 0, 0, 3, 0, 0,...

4, 0, 0, 0, 4, 0,...

5, 0, 0, 0, 0, 5,...

... The upper left term of M^n = A051296(n). - Gary W. Adamson, Sep 26 2011

Example

For n = 2, the 6 permutations are (2, 1), (-2, -1), (1, 2), (1, -2), (-1, 2), and (-1, -2).
a(3) = 22 = sum of top row terms of M^3 = (11 + 3 + 2 + 6); where 11 = A051296(3).

Maple

b := proc(n) option remember; if n = 0 then 2 else
add(factorial(k)*b(n-k), k=1..n) fi end:
a := n -> if n = 0 then return 1 else b(n) end:
seq(a(n), n=0..21); # Peter Luschny, Dec 07 2018

Crossrefs

Cf. A051296.

Sequence in context: A001861 A049526 A187251 * A301385 A093793 A087959

Adjacent sequences: A193760 A193761 A193762 * A193764 A193765 A193766

Keyword

nonn

Author

Andy Hardt, Aug 04 2011

Extensions

More terms from Joerg Arndt, Aug 16 2011.

Status

approved