A238914 Number of self-inverse permutations p on [n] where the maximal displacement of an element equals 3.

0, 0, 0, 0, 2, 7, 19, 47, 117, 284, 675, 1575, 3634, 8312, 18881, 42634, 95797, 214376, 478110, 1063242, 2358703, 5221606, 11538623, 25458412, 56095424, 123458153, 271440387, 596277224, 1308849869, 2871054209, 6294182153, 13791615999, 30206220592, 66131277054

Offset

0,5

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-1,-1,1,-4,-2,-3,-1,1,1,1).

Formula

G.f.: (x^3-x-2)*x^4 / ((x+1) *(x^6-x^5+x^4-3*x^3+3*x^2-3*x+1) *(x^4+x^3+x^2+x-1)).

Example

a(4) = 2: 4231, 4321.
a(5) = 7: 15342, 15432, 35142, 42315, 42513, 43215, 45312.
a(6) = 19: 126453, 126543, 146253, 153426, 153624, 154326, 156423, 216453, 216543, 351426, 351624, 423156, 423165, 425136, 426153, 432156, 432165, 453126, 456123.

Maple

gf:= (x^3-x-2)*x^4 / ((x+1)*(x^6-x^5+x^4-3*x^3+3*x^2-3*x+1)*
     (x^4+x^3+x^2+x-1)):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[(x^3 - x - 2) x^4/((x + 1) (x^6 - x^5 + x^4 - 3 x^3 + 3 x^2 - 3 x + 1) (x^4 + x^3 + x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 09 2014 *)
LinearRecurrence[{3, -1, -1, 1, -4, -2, -3, -1, 1, 1, 1}, {0, 0, 0, 0, 2, 7, 19, 47, 117, 284, 675}, 40] (* Harvey P. Dale, Jun 12 2021 *)

Crossrefs

Column k=3 of A238889.

Sequence in context: A209400 A112304 A006589 * A227946 A328990 A099484

Adjacent sequences: A238911 A238912 A238913 * A238915 A238916 A238917

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Mar 07 2014

Status

approved