A321048 Number of permutations of [n] with no fixed points where the maximal displacement of an element equals two.

0, 2, 3, 6, 12, 24, 44, 84, 159, 300, 564, 1064, 2004, 3774, 7107, 13386, 25208, 47472, 89400, 168360, 317055, 597080, 1124424, 2117520, 3987720, 7509690, 14142275, 26632782, 50154948, 94451976, 177872292, 334969724, 630816159, 1187955204, 2237161404

Offset: 2

Author

Alois P. Heinz, Oct 26 2018

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..2000
• Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,-2,1).

Crossrefs

Column k=2 of A259784.

Cf. A059841, A033305.

Formula

G.f.: (x-2)*x^3/((x-1)*(x+1)*(x^4-2*x^3+x^2-2*x+1)).

a(n) = A033305(n) - A059841(n).

a(n) = 2*a(n-1) - 2*a(n-5) + a(n-6). - Wesley Ivan Hurt, May 17 2023