OFFSET
0,3
COMMENTS
A signed permutation is a sequence (x_1,x_2,...,x_n) of integers such that {|x_1|,|x_2|,...|x_n|} = {1,2...,n}.
Adjacent elements that differ in sign will always differ by more than 1.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
FORMULA
A283184(n) = a(n) - a(n-1) for n > 0.
a(n) = (1+2*n)*a(n-1) + (3-2*n)*a(n-2) + (5-2*n)*a(n-3) + (-4+2*n)*a(n-4) for n >= 4.
EXAMPLE
In the following examples, the number of assignments of signs to each unsigned permutation is shown in parenthesis.
a(2) = 3: 123(1), 132(2). Total is 1 + 2 = 3.
a(3) = 17: 1234(1), 1243(2), 1324(4), 1342(4), 1423(4), 1432(2).
PROG
(PARI) a(n)=subst(serlaplace(polcoef(1/(1 + (1 - 2*y)*x + 2*y*x^2) + O(x*x^n), n)), y, 1)
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Mar 01 2024
STATUS
approved