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

2,2

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).

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

Crossrefs

Column k=2 of A259784.

Cf. A059841, A033305.

Sequence in context: A023675 A029996 A294123 * A038085 A124313 A049890

Adjacent sequences: A321045 A321046 A321047 * A321049 A321050 A321051

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 26 2018

Status

approved