A159715 Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.

4, 18, 72, 270, 972, 3402, 11664, 39366, 131220, 433026, 1417176, 4605822, 14880348, 47829690, 153055008, 487862838, 1549681956, 4907326194, 15496819560, 48814981614, 153418513644, 481176247338, 1506290861232, 4707158941350

Offset: 2

Author

R. H. Hardin, Apr 20 2009

Keywords

• nonn

Links

• R. H. Hardin, Table of n, a(n) for n = 2..100
• Index entries for linear recurrences with constant coefficients, signature (6,-9).

Crossrefs

Cf. A027261, A159721, A159727, A159733, A159736, A159738, A159739, A159740.

Programs

Magma

[2*n*3^(n-2): n in [2..30]]; // G. C. Greubel, Jun 01 2018

Mathematica

LinearRecurrence[{6,-9}, {}, 30] (* or *) Table[2*n*3^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *)

PARI

for(n=2, 30, print1(2*n*3^(n-2), ", ")) \\ G. C. Greubel, Jun 01 2018

Formula

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

Apparently a(n) = A027261(n-1), n > 2. - R. J. Mathar, Apr 21 2009

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

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

a(n) = 2*3^(n-2)*n for n>1.

a(n) = 6*a(n-1) - 9*a(n-2) for n>3. (End)

E.g.f.: 2*x*exp(3*x)/3. - G. C. Greubel, Jun 01 2018

From Amiram Eldar, May 16 2022: (Start)

Sum_{n>=2} 1/a(n) = (9/2)*log(3/2) - 3/2.

Sum_{n>=2} (-1)^n/a(n) = 3/2 - (9/2)*log(4/3). (End)