A159721 Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.

6, 36, 192, 960, 4608, 21504, 98304, 442368, 1966080, 8650752, 37748736, 163577856, 704643072, 3019898880, 12884901888, 54760833024, 231928233984, 979252543488, 4123168604160, 17317308137472, 72567767433216, 303465209266176

Offset

2,1

Links

R. H. Hardin, Table of n, a(n) for n = 2..100

Index entries for linear recurrences with constant coefficients, signature (8,-16).

Formula

a(n) = (copies*n)*(copies+1)^(n-2), here: copies = 3.

Conjectures from Colin Barker, Mar 23 2018: (Start)

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

a(n) = 3*4^(n-1)*(n+1).

a(n) = 8*a(n-1) - 16*a(n-2) for n>3. (End)

E.g.f.: 3*x*exp(4*x)/4. - G. C. Greubel, Jun 01 2018

From Amiram Eldar, May 16 2022: (Start)

Sum_{n>=2} 1/a(n) = (16/3)*log(4/3) - 3/2.

Sum_{n>=2} (-1)^n/a(n) = (16/3)*log(5/4) - 7/6. (End)

Mathematica

LinearRecurrence[{8, -16}, {6, 36}, 30] (* or *) Table[3*n*4^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *)

Prog

(PARI) for(n=2, 30, print1(3*n*4^(n-2), ", ")) \\ G. C. Greubel, Jun 01 2018
(Magma) [3*n*4^(n-2): n in [2..30]]; // G. C. Greubel, Jun 01 2018

Crossrefs

Cf. A159715, A159727, A159733, A159736, A159738, A159739, A159740.

Sequence in context: A366630 A209904 A146883 * A106539 A215453 A267229

Adjacent sequences: A159718 A159719 A159720 * A159722 A159723 A159724

Keyword

nonn,easy

Author

R. H. Hardin, Apr 20 2009

Status

approved