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A303649 Number of involutions of [n] having exactly one peak. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)