A303649 Number of involutions of [n] having exactly one peak.

0, 0, 0, 1, 6, 18, 44, 91, 172, 300, 496, 781, 1186, 1742, 2492, 3479, 4760, 6392, 8448, 11001, 14142, 17962, 22572, 28083, 34628, 42340, 51376, 61893, 74074, 88102, 104188, 122543, 143408, 167024, 193664, 223601, 257142, 294594, 336300, 382603, 433884, 490524

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Wikipedia, Involution

Index entries for linear recurrences with constant coefficients, signature (4,-4,-4,10,-4,-4,4,-1)

Formula

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

Example

a(3) = 1: 132.
a(4) = 6: 1243, 1324, 1432, 2143, 3412, 4231.
a(5) = 18: 12354, 12435, 12543, 13245, 14325, 14523, 15432, 21354, 21435, 21543, 32154, 34125, 42315, 42513, 45312, 52341, 52431, 53241.

Mathematica

LinearRecurrence[{4, -4, -4, 10, -4, -4, 4, -1}, {0, 0, 0, 1, 6, 18, 44, 91}, 50] (* Harvey P. Dale, Sep 17 2019 *)

Crossrefs

Column k=1 of A303648.

Cf. A000085.

Sequence in context: A136028 A083719 A182706 * A095170 A261647 A305031

Adjacent sequences: A303646 A303647 A303648 * A303650 A303651 A303652

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 27 2018

Status

approved