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A159721 Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum. 12
6, 36, 192, 960, 4608, 21504, 98304, 442368, 1966080, 8650752, 37748736, 163577856, 704643072, 3019898880, 12884901888, 54760833024, 231928233984, 979252543488, 4123168604160, 17317308137472, 72567767433216, 303465209266176 (list; graph; refs; listen; history; text; internal format)
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: A348568 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

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)