A323798 Number of permutations p of [n] such that max_{j=1..n} |p(j)-j| = 2.

0, 3, 9, 23, 60, 151, 366, 877, 2088, 4937, 11621, 27285, 63944, 149652, 349924, 817712, 1910027, 4460139, 10412815, 24306706, 56733689, 132411638, 309022917, 721175422, 1682988807, 3927486177, 9165229371, 21387927668, 49910484308, 116469784820, 271790117108

Offset

2,2

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (3,-1,0,-2,-3,1,1).

Formula

G.f.: x^3*(x^2-3)/((x^2+x-1)*(x^5-2*x^3-2*x+1)).

Example

a(3) = 3: 231, 312, 321.
a(4) = 9: 1342, 1423, 1432, 2314, 2413, 3124, 3142, 3214, 3412.
a(5) = 23: 12453, 12534, 12543, 13425, 13524, 14235, 14253, 14325, 14523, 21453, 21534, 21543, 23145, 23154, 24135, 24153, 31245, 31254, 31425, 31524, 32145, 32154, 34125.

Crossrefs

Column k=2 of A130152.

Sequence in context: A027058 A146818 A309301 * A180488 A318860 A318818

Adjacent sequences: A323795 A323796 A323797 * A323799 A323800 A323801

Keyword

nonn,easy

Author

Alois P. Heinz, Jan 28 2019

Status

approved